Finite Group Databasebeta

← C2×C7×#3484 #13239979

Subgroups — C2×C7×#3484 #13239979

Order 1792.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C24×C7×D4C211yesmaximal, characteristic, complemented
3C7×#3484C2132yesmaximal, direct product factor
4C2×C7×#546C218yesmaximal, complemented
5C2×C7×D42C218yesmaximal, complemented
6C2×C7×#535C212yesmaximal, complemented
7C2×C7×#534C214yesmaximal, complemented
8C2×C7×#525C212yesmaximal, complemented
9C22×C7×#120C214yesmaximal, complemented
10C2×C7×#518C211yesmaximal, characteristic, complemented
11C26×C7C2212yescomplemented
12C2×C7×H(5,𝔽2)—216no—
13C2×C7×H(5,𝔽2)C22116yescomplemented
14C22×C7×#41C2212yescomplemented
15C22×C7×#41C2214yescomplemented
16C23×C7×D4—216no—
17C23×C7×D4C2211yescharacteristic
18C23×C7×D4C2212yescomplemented
19C23×C7×D4C2211yescharacteristic, complemented
20C23×C7×D4C2218yescomplemented
21C23×C7×D4C2214yescomplemented
22C23×C7×D4C22116yescomplemented
23C23×C7×D4C2214yescomplemented
24C23×C7×D4C2218yescomplemented
25C24×C4×C7C2211yescharacteristic, complemented
26C7×#546C221128yescomplemented
27C7×D42C221128yescomplemented
28C7×#535C22132yescomplemented
29C7×#534C22164yescomplemented
30C2×C7×#127C2214yescomplemented
31C2×C7×#124C2214yescomplemented
32C7×#525C22132yescomplemented
33C2×C7×#123C2214yescomplemented
34C2×C7×#123C2218yescomplemented
35C2×C7×C22⋊Q8C2214yescomplemented
36C2×C7×#121C2214yescomplemented
37C2×C7×#121C22116yescomplemented
38C2×C7×#121C2218yescomplemented
39C2×C7×#120C2214yescomplemented
40C2×C7×#120C2218yescomplemented
41C2×C7×#120C22116yescomplemented
42C2×C7×#120C2218yescomplemented
43C2×C7×#120C22164yescomplemented
44C7×#518C22116yescomplemented
45C2×C4×C7×D4C2218yescomplemented
46C2×C4×C7×D4C2218yescomplemented
47C2×C7×#117C2212yescomplemented
48C22×C7×C22⋊C4C2214yescomplemented
49C22×C7×C22⋊C4C2218yescomplemented
50C2×#3484C711yesmaximal, characteristic, direct product factor, Sylow
51C25×C7—216no—
52C25×C7—416no—
53C25×C7C2311yescharacteristic
54C25×C7C2318yes—
55C25×C7C2312yes—
56C25×C7C2312yes—
57C25×C7C23116yescomplemented
58C25×C7C2314yescomplemented
59C7×H(5,𝔽2)—2128no—
60C2×C7×#41—232no—
61C2×C7×#41—216no—
62C2×C7×#41C23116yescomplemented
63C2×C7×#41C23132yescomplemented
64C22×C7×Q8C2312yescomplemented
65C22×C7×D4—216no—
66C22×C7×D4—232no—
67C22×C7×D4—264no—
68C22×C7×D4—2128no—
69C22×C7×D4—232no—
70C22×C7×D4—28no—
71C22×C7×D4—432no—
72C22×C7×D4D4116yescomplemented
73C22×C7×D4C2318yes—
74C22×C7×D4C2314yes—
75C22×C7×D4C2314yes—
76C22×C7×D4C2318yes—
77C22×C7×D4C2314yes—
78C22×C7×D4C2318yes—
79C22×C7×D4C23116yescomplemented
80C22×C7×D4C2318yescomplemented
81C22×C7×D4C23164yescomplemented
82C22×C7×D4C2318yescomplemented
83C22×C7×D4C2312yescomplemented
84C22×C7×D4C23116yescomplemented
85C22×C7×D4C23132yescomplemented
86C22×C7×D4C23132yescomplemented
87C22×C7×D4C23164yescomplemented
88C23×C4×C7—28no—
89C23×C4×C7C2314yes—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2318yescomplemented
93C23×C4×C7C2314yescomplemented
94C23×C4×C7C2314yescomplemented
95C23×C4×C7C2318yescomplemented
96C7×#127C23132yescomplemented
97C7×#124C23132yescomplemented
98C7×#123C23132yescomplemented
99C7×#123C23164yescomplemented
100C7×C22⋊Q8C23132yescomplemented
101C7×#121C23132yescomplemented
102C7×#121C231128yescomplemented
103C7×#121C23164yescomplemented
104C7×#120C23132yescomplemented
105C7×#120C23164yescomplemented
106C7×#120C231128yescomplemented
107C7×#120C23164yescomplemented
108C4×C7×D4C23164yescomplemented
109C4×C7×D4C23164yescomplemented
110C7×#117C23116yescomplemented
111C2×C7×C4⋊C4C2314yescomplemented
112C2×C7×C4⋊C4C2318yescomplemented
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2318yes—
115C2×C7×C22⋊C4C23132yescomplemented
116C2×C7×C22⋊C4C23164yescomplemented
117C2×C7×C22⋊C4C2318yescomplemented
118C2×C7×C22⋊C4C23116yescomplemented
119C2×C7×C22⋊C4C2318yescomplemented
120C2×C42×C7C2314yescomplemented
121C22×H(5,𝔽2)C2×C711yescharacteristic, complemented
122C24×D4C2×C711yescharacteristic, complemented
123#3484C2×C7132yesdirect product factor
124C2×#546C2×C718yescomplemented
125C2×D42C2×C718yescomplemented
126C2×#535C2×C712yescomplemented
127C2×#534C2×C714yescomplemented
128C2×#525C2×C712yescomplemented
129C22×#120C2×C714yescomplemented
130C2×#518C2×C711yescharacteristic, complemented
131C24×C7—24no—
132C24×C7—28no—
133C24×C7—232no—
134C24×C7—28no—
135C24×C7—264no—
136C24×C7—232no—
137C24×C7—216no—
138C24×C7—48no—
139C24×C7—416no—
140C24×C7—48no—
141C24×C7—464no—
142C24×C7—416no—
143C24×C7—4128no—
144C24×C7C2×D4116yescomplemented
145C24×C7C2414yes—
146C24×C7C2414yes—
147C24×C7C2414yes—
148C24×C7C24132yes—
149C24×C7C2411yescharacteristic
150C24×C7C2414yes—
151C24×C7C2412yes—
152C24×C7C2418yes—
153C24×C7C2418yes—
154C24×C7C24116yescomplemented
155C7×#41—2128no—
156C7×#41—264no—
157C2×C7×Q8—28no—
158C2×C7×Q8C2418yescomplemented
159C2×C7×D4—232no—
160C2×C7×D4—216no—
161C2×C7×D4—232no—
162C2×C7×D4—264no—
163C2×C7×D4—2128no—
164C2×C7×D4—232no—
165C2×C7×D4—2256no—
166C2×C7×D4—2128no—
167C2×C7×D4—216no—
168C2×C7×D4—28no—
169C2×C7×D4—232no—
170C2×C7×D4—432no—
171C2×C7×D4—4128no—
172C2×C7×D4C2×D4132yescomplemented
173C2×C7×D4C2×D4164yescomplemented
174C2×C7×D4C24132yes—
175C2×C7×D4C24116yes—
176C2×C7×D4C24132yes—
177C2×C7×D4C24116yes—
178C2×C7×D4C24116yes—
179C2×C7×D4C24132yescomplemented
180C2×C7×D4C2418yescomplemented
181C2×C7×D4C24164yescomplemented
182C22×C4×C7—24no—
183C22×C4×C7—216no—
184C22×C4×C7—216no—
185C22×C4×C7—216no—
186C22×C4×C7—232no—
187C22×C4×C7—416no—
188C22×C4×C7C2×D418yescomplemented
189C22×C4×C7C24116yes—
190C22×C4×C7C2414yes—
191C22×C4×C7C2418yes—
192C22×C4×C7C2414yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2414yes—
196C22×C4×C7C24116yescomplemented
197C22×C4×C7C24116yescomplemented
198C22×C4×C7C24132yescomplemented
199C7×C4⋊C4C24116yescomplemented
200C7×C4⋊C4C24132yescomplemented
201C7×C22⋊C4C24116yes—
202C7×C22⋊C4C24132yes—
203C7×C22⋊C4C24132yescomplemented
204C7×C22⋊C4C24164yescomplemented
205C7×C22⋊C4C24132yescomplemented
206C42×C7C24116yescomplemented
207C26C22×C712yescomplemented
208C2×H(5,𝔽2)—216no—
209C2×H(5,𝔽2)C22×C7116yescomplemented
210C22×#41C22×C712yescomplemented
211C22×#41C22×C714yescomplemented
212C23×D4—216no—
213C23×D4C22×C711yescharacteristic
214C23×D4C22×C712yescomplemented
215C23×D4C22×C711yescharacteristic, complemented
216C23×D4C22×C718yescomplemented
217C23×D4C22×C714yescomplemented
218C23×D4C22×C7116yescomplemented
219C23×D4C22×C714yescomplemented
220C23×D4C22×C718yescomplemented
221C24×C4C22×C711yescharacteristic, complemented
222#546C22×C71128yescomplemented
223D42C22×C71128yescomplemented
224#535C22×C7132yescomplemented
225#534C22×C7164yescomplemented
226C2×#127C22×C714yescomplemented
227C2×#124C22×C714yescomplemented
228#525C22×C7132yescomplemented
229C2×#123C22×C714yescomplemented
230C2×#123C22×C718yescomplemented
231C2×C22⋊Q8C22×C714yescomplemented
232C2×#121C22×C714yescomplemented
233C2×#121C22×C7116yescomplemented
234C2×#121C22×C718yescomplemented
235C2×#120C22×C714yescomplemented
236C2×#120C22×C718yescomplemented
237C2×#120C22×C7116yescomplemented
238C2×#120C22×C718yescomplemented
239C2×#120C22×C7164yescomplemented
240#518C22×C7116yescomplemented
241C2×C4×D4C22×C718yescomplemented
242C2×C4×D4C22×C718yescomplemented
243C2×#117C22×C712yescomplemented
244C22×C22⋊C4C22×C714yescomplemented
245C22×C22⋊C4C22×C718yescomplemented
246C23×C7—232no—
247C23×C7—28no—
248C23×C7—24no—
249C23×C7—216no—
250C23×C7—24no—
251C23×C7—24no—
252C23×C7—216no—
253C23×C7—28no—
254C23×C7—264no—
255C23×C7—216no—
256C23×C7—28no—
257C23×C7—216no—
258C23×C7—216no—
259C23×C7—264no—
260C23×C7—232no—
261C23×C7—432no—
262C23×C7—416no—
263C23×C7—432no—
264C23×C7—416no—
265C23×C7—432no—
266C23×C7—4128no—
267C23×C7—4256no—
268C23×C7—432no—
269C23×C7—832no—
270C23×C7C22×D414yes—
271C23×C7C22×D4116yes—
272C23×C7C22×D4132yescomplemented
273C23×C7H(5,𝔽2)18yescomplemented
274C23×C7C2518yes—
275C23×C7C2518yes—
276C23×C7C2512yes—
277C23×C7C2518yes—
278C23×C7C2514yes—
279C23×C7C2511yescharacteristic
280C7×Q8—216no—
281C7×D4—264no—
282C7×D4—232no—
283C7×D4—264no—
284C7×D4—264no—
285C7×D4—232no—
286C7×D4—216no—
287C7×D4—464no—
288C7×D4C22×D4164yescomplemented
289C2×C4×C7—28no—
290C2×C4×C7—24no—
291C2×C4×C7—28no—
292C2×C4×C7—232no—
293C2×C4×C7—216no—
294C2×C4×C7—232no—
295C2×C4×C7—232no—
296C2×C4×C7—432no—
297C2×C4×C7C22×D418yes—
298C2×C4×C7C22×D4116yescomplemented
299C2×C4×C7C25116yes—
300C2×C4×C7C2518yes—
301C2×C4×C7C2514yes—
302C2×C4×C7C2514yes—
303C25—216no—
304C25—416no—
305C25C23×C711yescharacteristic
306C25C23×C718yes—
307C25C23×C712yes—
308C25C23×C712yes—
309C25C23×C7116yescomplemented
310C25C23×C714yescomplemented
311H(5,𝔽2)—2128no—
312C2×#41—232no—
313C2×#41—216no—
314C2×#41C23×C7116yescomplemented
315C2×#41C23×C7132yescomplemented
316C22×Q8C23×C712yescomplemented
317C22×D4—216no—
318C22×D4—232no—
319C22×D4—264no—
320C22×D4—2128no—
321C22×D4—232no—
322C22×D4—28no—
323C22×D4—432no—
324C22×D4C7×D4116yescomplemented
325C22×D4C23×C718yes—
326C22×D4C23×C714yes—
327C22×D4C23×C718yes—
328C22×D4C23×C714yes—
329C22×D4C23×C714yes—
330C22×D4C23×C718yes—
331C22×D4C23×C7116yescomplemented
332C22×D4C23×C718yescomplemented
333C22×D4C23×C7164yescomplemented
334C22×D4C23×C718yescomplemented
335C22×D4C23×C712yescomplemented
336C22×D4C23×C7116yescomplemented
337C22×D4C23×C7132yescomplemented
338C22×D4C23×C7132yescomplemented
339C22×D4C23×C7164yescomplemented
340C23×C4—28no—
341C23×C4C23×C714yes—
342C23×C4C23×C711yescharacteristic
343C23×C4C23×C711yescharacteristic
344C23×C4C23×C718yescomplemented
345C23×C4C23×C714yescomplemented
346C23×C4C23×C714yescomplemented
347C23×C4C23×C718yescomplemented
348#127C23×C7132yescomplemented
349#124C23×C7132yescomplemented
350#123C23×C7132yescomplemented
351#123C23×C7164yescomplemented
352C22⋊Q8C23×C7132yescomplemented
353#121C23×C7132yescomplemented
354#121C23×C71128yescomplemented
355#121C23×C7164yescomplemented
356#120C23×C7132yescomplemented
357#120C23×C7164yescomplemented
358#120C23×C71128yescomplemented
359#120C23×C7164yescomplemented
360C4×D4C23×C7164yescomplemented
361C4×D4C23×C7164yescomplemented
362#117C23×C7116yescomplemented
363C2×C4⋊C4C23×C714yescomplemented
364C2×C4⋊C4C23×C718yescomplemented
365C2×C22⋊C4C23×C714yes—
366C2×C22⋊C4C23×C718yes—
367C2×C22⋊C4C23×C7132yescomplemented
368C2×C22⋊C4C23×C7164yescomplemented
369C2×C22⋊C4C23×C718yescomplemented
370C2×C22⋊C4C23×C7116yescomplemented
371C2×C22⋊C4C23×C718yescomplemented
372C2×C42C23×C714yescomplemented
373C22×C7—232no—
374C22×C7—24no—
375C22×C7—216no—
376C22×C7—24no—
377C22×C7—24no—
378C22×C7—28no—
379C22×C7—216no—
380C22×C7—232no—
381C22×C7—28no—
382C22×C7—28no—
383C22×C7—216no—
384C22×C7—216no—
385C22×C7—432no—
386C22×C7—4128no—
387C22×C7—432no—
388C22×C7—416no—
389C22×C7—416no—
390C22×C7—832no—
391C22×C7C23×D414yes—
392C22×C7C23×D4116yes—
393C22×C7C23×D412yes—
394C22×C7C2×H(5,𝔽2)14yes—
395C22×C7C2×H(5,𝔽2)18yescomplemented
396C22×C7C2611yescharacteristic
397C4×C7—24no—
398C4×C7—28no—
399C4×C7—216no—
400C4×C7C23×D418yes—
401C24—24no—
402C24—28no—
403C24—232no—
404C24—28no—
405C24—264no—
406C24—232no—
407C24—216no—
408C24—48no—
409C24—416no—
410C24—48no—
411C24—464no—
412C24—416no—
413C24—4128no—
414C24C2×C7×D4116yescomplemented
415C24C24×C714yes—
416C24C24×C714yes—
417C24C24×C714yes—
418C24C24×C7132yes—
419C24C24×C711yescharacteristic
420C24C24×C714yes—
421C24C24×C712yes—
422C24C24×C718yes—
423C24C24×C718yes—
424C24C24×C7116yescomplemented
425#41—2128no—
426#41—264no—
427C2×Q8—28no—
428C2×Q8C24×C718yescomplemented
429C2×D4—232no—
430C2×D4—216no—
431C2×D4—232no—
432C2×D4—264no—
433C2×D4—2128no—
434C2×D4—232no—
435C2×D4—2256no—
436C2×D4—2128no—
437C2×D4—216no—
438C2×D4—28no—
439C2×D4—232no—
440C2×D4—432no—
441C2×D4—4128no—
442C2×D4C2×C7×D4132yescomplemented
443C2×D4C2×C7×D4164yescomplemented
444C2×D4C24×C7132yes—
445C2×D4C24×C7116yes—
446C2×D4C24×C7132yes—
447C2×D4C24×C7116yes—
448C2×D4C24×C7116yes—
449C2×D4C24×C7132yescomplemented
450C2×D4C24×C718yescomplemented
451C2×D4C24×C7164yescomplemented
452C22×C4—24no—
453C22×C4—216no—
454C22×C4—216no—
455C22×C4—216no—
456C22×C4—232no—
457C22×C4—416no—
458C22×C4C2×C7×D418yescomplemented
459C22×C4C24×C718yes—
460C22×C4C24×C714yes—
461C22×C4C24×C712yes—
462C22×C4C24×C7116yes—
463C22×C4C24×C714yes—
464C22×C4C24×C712yes—
465C22×C4C24×C714yes—
466C22×C4C24×C7116yescomplemented
467C22×C4C24×C7116yescomplemented
468C22×C4C24×C7132yescomplemented
469C4⋊C4C24×C7116yescomplemented
470C4⋊C4C24×C7132yescomplemented
471C22⋊C4C24×C7116yes—
472C22⋊C4C24×C7132yes—
473C22⋊C4C24×C7132yescomplemented
474C22⋊C4C24×C7164yescomplemented
475C22⋊C4C24×C7132yescomplemented
476C42C24×C7116yescomplemented
477C2×C7—24no—
478C2×C7—28no—
479C2×C7—216no—
480C2×C7—48no—
481C2×C7—48no—
482C2×C7#348414yesdirect product factor
483C2×C7C24×D411yescharacteristic
484C2×C7C22×H(5,𝔽2)12yes—
485C23—232no—
486C23—28no—
487C23—24no—
488C23—216no—
489C23—24no—
490C23—24no—
491C23—216no—
492C23—28no—
493C23—264no—
494C23—216no—
495C23—28no—
496C23—216no—
497C23—216no—
498C23—264no—
499C23—232no—
500C23—432no—
501C23—416no—
502C23—432no—
503C23—416no—
504C23—432no—
505C23—4128no—
506C23—4256no—
507C23—432no—
508C23—832no—
509C23C22×C7×D414yes—
510C23C22×C7×D4116yes—
511C23C22×C7×D4132yescomplemented
512C23C7×H(5,𝔽2)18yescomplemented
513C23C25×C718yes—
514C23C25×C718yes—
515C23C25×C712yes—
516C23C25×C718yes—
517C23C25×C714yes—
518C23C25×C711yescharacteristic
519Q8—216no—
520D4—264no—
521D4—232no—
522D4—264no—
523D4—264no—
524D4—232no—
525D4—216no—
526D4—464no—
527D4C22×C7×D4164yescomplemented
528C2×C4—28no—
529C2×C4—24no—
530C2×C4—28no—
531C2×C4—232no—
532C2×C4—216no—
533C2×C4—232no—
534C2×C4—232no—
535C2×C4—432no—
536C2×C4C22×C7×D418yes—
537C2×C4C22×C7×D4116yescomplemented
538C2×C4C25×C7116yes—
539C2×C4C25×C718yes—
540C2×C4C25×C714yes—
541C2×C4C25×C714yes—
542C7C2×#348411yescharacteristic, direct product factor, Sylow
543C22—232no—
544C22—24no—
545C22—216no—
546C22—24no—
547C22—24no—
548C22—28no—
549C22—216no—
550C22—232no—
551C22—28no—
552C22—28no—
553C22—216no—
554C22—216no—
555C22—432no—
556C22—4128no—
557C22—432no—
558C22—416no—
559C22—416no—
560C22—832no—
561C22C23×C7×D414yes—
562C22C23×C7×D4116yes—
563C22C23×C7×D412yes—
564C22C2×C7×H(5,𝔽2)14yes—
565C22C2×C7×H(5,𝔽2)18yescomplemented
566C22C26×C711yescharacteristic
567C4—24no—
568C4—28no—
569C4—216no—
570C4C23×C7×D418yes—
571C2—24no—
572C2—28no—
573C2—216no—
574C2—48no—
575C2—48no—
576C2C7×#348414yesdirect product factor
577C2C24×C7×D411yescharacteristic
578C2C22×C7×H(5,𝔽2)12yes—
subgroupG/H
center, socleC23×C7C25
commutator, Frattini, cosocleC22C26×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C7×H(5,𝔽2)C2semidirect
2. C24×C7×D4C2semidirect
3. C7×#3484C2direct (N × H)
4. C2×C7×#546C2semidirect
5. C2×C7×D42C2semidirect
6. C2×C7×#535C2semidirect
7. C2×C7×#534C2semidirect
8. C2×C7×#525C2semidirect
9. C22×C7×#120C2semidirect
10. C2×C7×#518C2semidirect
11. C26×C7C22semidirect
13. C2×C7×H(5,𝔽2)C22semidirect
14. C22×C7×#41C22semidirect
15. C22×C7×#41C22semidirect
18. C23×C7×D4C22semidirect
19. C23×C7×D4C22semidirect
20. C23×C7×D4C22semidirect
21. C23×C7×D4C22semidirect
22. C23×C7×D4C22semidirect
23. C23×C7×D4C22semidirect
24. C23×C7×D4C22semidirect
25. C24×C4×C7C22semidirect
26. C7×#546C22semidirect
27. C7×D42C22semidirect
28. C7×#535C22semidirect
29. C7×#534C22semidirect
30. C2×C7×#127C22semidirect
31. C2×C7×#124C22semidirect
32. C7×#525C22semidirect
33. C2×C7×#123C22semidirect
34. C2×C7×#123C22semidirect
35. C2×C7×C22⋊Q8C22semidirect
36. C2×C7×#121C22semidirect
37. C2×C7×#121C22semidirect
38. C2×C7×#121C22semidirect
39. C2×C7×#120C22semidirect
40. C2×C7×#120C22semidirect
41. C2×C7×#120C22semidirect
42. C2×C7×#120C22semidirect
43. C2×C7×#120C22semidirect
44. C7×#518C22semidirect
45. C2×C4×C7×D4C22semidirect
46. C2×C4×C7×D4C22semidirect
47. C2×C7×#117C22semidirect
48. C22×C7×C22⋊C4C22semidirect
49. C22×C7×C22⋊C4C22semidirect
50. C2×#3484C7direct (N × H)
57. C25×C7C23semidirect
58. C25×C7C23semidirect
62. C2×C7×#41C23semidirect
63. C2×C7×#41C23semidirect
64. C22×C7×Q8C23semidirect
72. C22×C7×D4D4semidirect
79. C22×C7×D4C23semidirect
80. C22×C7×D4C23semidirect
81. C22×C7×D4C23semidirect
82. C22×C7×D4C23semidirect
83. C22×C7×D4C23semidirect
84. C22×C7×D4C23semidirect
85. C22×C7×D4C23semidirect
86. C22×C7×D4C23semidirect
87. C22×C7×D4C23semidirect
92. C23×C4×C7C23semidirect
93. C23×C4×C7C23semidirect
94. C23×C4×C7C23semidirect
95. C23×C4×C7C23semidirect
96. C7×#127C23semidirect
97. C7×#124C23semidirect
98. C7×#123C23semidirect
99. C7×#123C23semidirect
100. C7×C22⋊Q8C23semidirect
101. C7×#121C23semidirect
102. C7×#121C23semidirect
103. C7×#121C23semidirect
104. C7×#120C23semidirect
105. C7×#120C23semidirect
106. C7×#120C23semidirect
107. C7×#120C23semidirect
108. C4×C7×D4C23semidirect
109. C4×C7×D4C23semidirect
110. C7×#117C23semidirect
111. C2×C7×C4⋊C4C23semidirect
112. C2×C7×C4⋊C4C23semidirect
115. C2×C7×C22⋊C4C23semidirect
116. C2×C7×C22⋊C4C23semidirect
117. C2×C7×C22⋊C4C23semidirect
118. C2×C7×C22⋊C4C23semidirect
119. C2×C7×C22⋊C4C23semidirect
120. C2×C42×C7C23semidirect
121. C22×H(5,𝔽2)C2×C7semidirect
122. C24×D4C2×C7semidirect
123. #3484C2×C7direct (N × H)
124. C2×#546C2×C7semidirect
125. C2×D42C2×C7semidirect
126. C2×#535C2×C7semidirect
127. C2×#534C2×C7semidirect
128. C2×#525C2×C7semidirect
129. C22×#120C2×C7semidirect
130. C2×#518C2×C7semidirect
144. C24×C7C2×D4semidirect
154. C24×C7C24semidirect
158. C2×C7×Q8C24semidirect
172. C2×C7×D4C2×D4semidirect
173. C2×C7×D4C2×D4semidirect
179. C2×C7×D4C24semidirect
180. C2×C7×D4C24semidirect
181. C2×C7×D4C24semidirect
188. C22×C4×C7C2×D4semidirect
196. C22×C4×C7C24semidirect
197. C22×C4×C7C24semidirect
198. C22×C4×C7C24semidirect
199. C7×C4⋊C4C24semidirect
200. C7×C4⋊C4C24semidirect
203. C7×C22⋊C4C24semidirect
204. C7×C22⋊C4C24semidirect
205. C7×C22⋊C4C24semidirect
206. C42×C7C24semidirect
207. C26C22×C7semidirect
209. C2×H(5,𝔽2)C22×C7semidirect
210. C22×#41C22×C7semidirect
211. C22×#41C22×C7semidirect
214. C23×D4C22×C7semidirect
215. C23×D4C22×C7semidirect
216. C23×D4C22×C7semidirect
217. C23×D4C22×C7semidirect
218. C23×D4C22×C7semidirect
219. C23×D4C22×C7semidirect
220. C23×D4C22×C7semidirect
221. C24×C4C22×C7semidirect
222. #546C22×C7semidirect
223. D42C22×C7semidirect
224. #535C22×C7semidirect
225. #534C22×C7semidirect
226. C2×#127C22×C7semidirect
227. C2×#124C22×C7semidirect
228. #525C22×C7semidirect
229. C2×#123C22×C7semidirect
230. C2×#123C22×C7semidirect
231. C2×C22⋊Q8C22×C7semidirect
232. C2×#121C22×C7semidirect
233. C2×#121C22×C7semidirect
234. C2×#121C22×C7semidirect
235. C2×#120C22×C7semidirect
236. C2×#120C22×C7semidirect
237. C2×#120C22×C7semidirect
238. C2×#120C22×C7semidirect
239. C2×#120C22×C7semidirect
240. #518C22×C7semidirect
241. C2×C4×D4C22×C7semidirect
242. C2×C4×D4C22×C7semidirect
243. C2×#117C22×C7semidirect
244. C22×C22⋊C4C22×C7semidirect
245. C22×C22⋊C4C22×C7semidirect
272. C23×C7C22×D4semidirect
273. C23×C7H(5,𝔽2)semidirect
288. C7×D4C22×D4semidirect
298. C2×C4×C7C22×D4semidirect
309. C25C23×C7semidirect
310. C25C23×C7semidirect
314. C2×#41C23×C7semidirect
315. C2×#41C23×C7semidirect
316. C22×Q8C23×C7semidirect
324. C22×D4C7×D4semidirect
331. C22×D4C23×C7semidirect
332. C22×D4C23×C7semidirect
333. C22×D4C23×C7semidirect
334. C22×D4C23×C7semidirect
335. C22×D4C23×C7semidirect
336. C22×D4C23×C7semidirect
337. C22×D4C23×C7semidirect
338. C22×D4C23×C7semidirect
339. C22×D4C23×C7semidirect
344. C23×C4C23×C7semidirect
345. C23×C4C23×C7semidirect
346. C23×C4C23×C7semidirect
347. C23×C4C23×C7semidirect
348. #127C23×C7semidirect
349. #124C23×C7semidirect
350. #123C23×C7semidirect
351. #123C23×C7semidirect
352. C22⋊Q8C23×C7semidirect
353. #121C23×C7semidirect
354. #121C23×C7semidirect
355. #121C23×C7semidirect
356. #120C23×C7semidirect
357. #120C23×C7semidirect
358. #120C23×C7semidirect
359. #120C23×C7semidirect
360. C4×D4C23×C7semidirect
361. C4×D4C23×C7semidirect
362. #117C23×C7semidirect
363. C2×C4⋊C4C23×C7semidirect
364. C2×C4⋊C4C23×C7semidirect
367. C2×C22⋊C4C23×C7semidirect
368. C2×C22⋊C4C23×C7semidirect
369. C2×C22⋊C4C23×C7semidirect
370. C2×C22⋊C4C23×C7semidirect
371. C2×C22⋊C4C23×C7semidirect
372. C2×C42C23×C7semidirect
395. C22×C7C2×H(5,𝔽2)semidirect
414. C24C2×C7×D4semidirect
424. C24C24×C7semidirect
428. C2×Q8C24×C7semidirect
442. C2×D4C2×C7×D4semidirect
443. C2×D4C2×C7×D4semidirect
449. C2×D4C24×C7semidirect
450. C2×D4C24×C7semidirect
451. C2×D4C24×C7semidirect
458. C22×C4C2×C7×D4semidirect
466. C22×C4C24×C7semidirect
467. C22×C4C24×C7semidirect
468. C22×C4C24×C7semidirect
469. C4⋊C4C24×C7semidirect
470. C4⋊C4C24×C7semidirect
473. C22⋊C4C24×C7semidirect
474. C22⋊C4C24×C7semidirect
475. C22⋊C4C24×C7semidirect
476. C42C24×C7semidirect
482. C2×C7#3484direct (N × H)
511. C23C22×C7×D4semidirect
512. C23C7×H(5,𝔽2)semidirect
527. D4C22×C7×D4semidirect
537. C2×C4C22×C7×D4semidirect
542. C7C2×#3484direct (N × H)
565. C22C2×C7×H(5,𝔽2)semidirect
576. C2C7×#3484direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C7×H(5,𝔽2)2
C24×C7×D42
C7×#34842
C2×C7×#5462
C2×C7×D422
C2×C7×#5352
C2×C7×#5342
C2×C7×#5252
C22×C7×#1202
C2×C7×#5182
C2×#34847