Finite Group Databasebeta

← C2×#11740297 #13521649

Subgroups — C2×#11740297 #13521649

Order 1792.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#123C211yesmaximal, characteristic, complemented
2C22×#6499C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
4C22×#6459C211yesmaximal, characteristic, complemented
5C2×#89995C211yesmaximal, characteristic
6C2×#89982C211yesmaximal, characteristic, complemented
7#11740297C2116yesmaximal, direct product factor
8C2×#89751C211yesmaximal, characteristic, complemented
9C2×#89762C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
11C2×#89728C211yesmaximal, characteristic, complemented
12C2×#89720C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14C2×#89729C211yesmaximal, characteristic, complemented
15C2×#89717C211yesmaximal, characteristic, complemented
16C2×#89717C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C4×D7C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C2×C7×#123—28no—
24C2×C7×#123C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C4⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C22×C22⋊Dic7C2211yescharacteristic
36C2×#6499—28no—
37C2×#6499C2218yescomplemented
38C2×C4×C22⋊D7—28no—
39C2×C4×C22⋊D7C2218yescomplemented
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×(C2×D7)⋊C4C2211yescharacteristic
44C22×C4⋊Dic7C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C22×C4×Dic7C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C2×#6459—28no—
53C2×#6459C2218yescomplemented
54#89995C2218yes—
55#89982C2218yescomplemented
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89762C2218yescomplemented
63#89751C2218yescomplemented
64C4⋊C4×Dic7C2218yescomplemented
65#89733C2218yescomplemented
66#89729C2218yescomplemented
67#89728C2218yescomplemented
68#89720C2218yescomplemented
69#89717C2218yescomplemented
70#89717C2218yescomplemented
71C2×#2461—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—42no—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—42no—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2314yes—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C22×C22⋊D7—24no—
89C22×C22⋊D7—24no—
90C22×C22⋊D7—24no—
91C22×C22⋊D7—24no—
92C22×C22⋊D7—24no—
93C22×C22⋊D7—42no—
94C22×C22⋊D7C2314yes—
95C22×C22⋊D7C2314yes—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C22×C4×D7—24no—
104C22×C4×D7—24no—
105C22×C4×D7—42no—
106C22×C4×D7C2314yes—
107C22×Dic14—24no—
108C22×Dic14—24no—
109C22×Dic14—42no—
110C22×Dic14C2314yes—
111C7×#123—232no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4D418yescomplemented
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C4⋊C4C2314yes—
116C2×C7×C22⋊C4—24no—
117C2×C7×C22⋊C4—24no—
118C2×C7×C22⋊C4—24no—
119C2×C7×C22⋊C4C2314yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—24no—
126C2×C22⋊Dic7—24no—
127C2×C22⋊Dic7D418yescomplemented
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132C2×C22⋊Dic7C2314yes—
133C2×C22⋊Dic7C2314yes—
134#6499—232no—
135C4×C22⋊D7—232no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—24no—
138C2×(C2×D7)⋊C4—24no—
139C2×(C2×D7)⋊C4—24no—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×C4⋊Dic7—24no—
145C2×C4⋊Dic7C2314yes—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—42no—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7—24no—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159C2×C4×Dic7C2314yes—
160#6459—232no—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#124—71no—
168C22×#123D711yescharacteristic, complemented
169C22×C22⋊Q8—71no—
170C22×C4×D4—71no—
171#2461—716no—
172C2×#396—71no—
173C2×#395—71no—
174C2×#394—71no—
175C2×#392—71no—
176C2×#390—71no—
177C2×#388—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#386—71no—
181C2×#385—71no—
182C2×C4×C4⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7C2×D414yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7#4114yes—
207C23×D7C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—44no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—28no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—28no—
226C22×C4×C7—44no—
227C22×C4×C7—416no—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2×D414yes—
230C22×C4×C7C2×D414yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2412yes—
235C22×C4×C7C2412yes—
236C2×C22⋊D7—232no—
237C2×C22⋊D7—28no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C2×C22⋊D7—28no—
241C2×C22⋊D7—28no—
242C2×C22⋊D7—44no—
243C2×C22⋊D7—416no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—22no—
257C22×Dic7—22no—
258C22×Dic7—22no—
259C22×Dic7—22no—
260C22×Dic7—22no—
261C22×Dic7C2×D414yes—
262C22×Dic7C2×D414yes—
263C22×Dic7#4114yes—
264C22×Dic7#4114yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×C4×D7—28no—
273C2×C4×D7—28no—
274C2×C4×D7—44no—
275C2×C4×D7—416no—
276C2×Dic14—28no—
277C2×Dic14—28no—
278C2×Dic14—44no—
279C2×Dic14—416no—
280C7×C4⋊C4—28no—
281C7×C4⋊C4C2×D4116yescomplemented
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—28no—
290C22⋊Dic7C2×D4116yescomplemented
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—28no—
295C4⋊Dic7—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—44no—
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×Q8—71no—
304C23×D4—71no—
305C23×D4—71no—
306C23×D4C2×D711yescharacteristic
307C24×C4—71no—
308C24×C4C2×D711yescharacteristic
309C2×#124—78no—
310C2×#124—148no—
311C2×#123—28no—
312C2×#123C2×D718yescomplemented
313C2×C22⋊Q8—78no—
314C2×C22⋊Q8—148no—
315C2×C4×D4—78no—
316C2×C4×D4—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4C2×D711yescharacteristic
323C22×C4⋊C4C2×D711yescharacteristic
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#396—78no—
341#395—78no—
342#394—78no—
343#392—78no—
344#390—78no—
345#388—78no—
346#388—78no—
347#388—78no—
348#386—78no—
349#385—78no—
350C4×C4⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7C22×D414yes—
385C23×C7C22×D412yes—
386C23×C7C22×D412yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C72−1+412yes—
392C23×C7C2511yescharacteristic
393C22×D7—28no—
394C22×D7—28no—
395C22×D7—28no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7C2×#4114yes—
407C7×D4—416no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—416no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C22×D414yes—
429C22⋊D7—232no—
430C22⋊D7—416no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—28no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—44no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457C2×Dic7C2×#4114yes—
458C2×Dic7C2×#4114yes—
459C4×D7—416no—
460Dic14—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×Q8—74no—
465C22×Q8—144no—
466C22×Q8—144no—
467C22×Q8—282no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—74no—
472C22×D4—74no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—144no—
476C22×D4—144no—
477C22×D4—144no—
478C22×D4—282no—
479C22×D4C22×D714yes—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—74no—
491C23×C4—144no—
492C23×C4—144no—
493C23×C4—282no—
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D714yes—
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#124—1432no—
501#123—232no—
502C22⋊Q8—1432no—
503C4×D4—1432no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—282no—
515C2×C4⋊C4C22⋊D718yescomplemented
516C2×C4⋊C4C22×D714yes—
517C2×C4⋊C4C22×D714yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—78no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—144no—
538C2×C22⋊C4—144no—
539C2×C22⋊C4—144no—
540C2×C22⋊C4—144no—
541C2×C22⋊C4C22×D714yes—
542C2×C22⋊C4C22×D714yes—
543C2×C22⋊C4C22×D714yes—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—74no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95—74no—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—416no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—88no—
572C22×C7#52514yes—
573C22×C7#53214yes—
574C22×C7#54214yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54814yes—
578C22×C7#55114yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×2−1+411yescharacteristic
586C2×D7—24no—
587C2×D7—24no—
588C2×D7—24no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—416no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—24no—
603Dic7—42no—
604Dic7—42no—
605Dic7—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—74no—
620C24—72no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24D4×D714yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×Q8—148no—
632C2×Q8—148no—
633C2×Q8—284no—
634C2×Q8—2816no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—44no—
638C2×D4—416no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—148no—
642C2×D4—1432no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—284no—
646C2×D4—2816no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—44no—
662C22×C4—416no—
663C22×C4—74no—
664C22×C4—74no—
665C22×C4—74no—
666C22×C4—74no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—148no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—148no—
693C22×C4—284no—
694C22×C4—2816no—
695C22×C4C2×C22⋊D714yes—
696C22×C4C2×C22⋊D714yes—
697C22×C4C2×C22⋊D714yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—28no—
704C4⋊C4—148no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C4⋊C4—284no—
709C4⋊C4C2×C22⋊D7116yescomplemented
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—716no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—148no—
722C22⋊C4—148no—
723C42—148no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—82no—
728C2×C7#246118yescomplemented
729C2×C7C2×#52511yescharacteristic
730C2×C7C2×#53211yescharacteristic
731C2×C7C2×#54211yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54811yescharacteristic
735C2×C7C2×#55111yescharacteristic
736D7—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—74no—
765C23—148no—
766C23—148no—
767C23—148no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—142no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23—284no—
778C23C2×D4×D714yes—
779C23C2×D4×D712yes—
780C23#654812yes—
781C23D7×#4112yes—
782C23D7×#4112yes—
783C23D7×#4112yes—
784C23#655412yes—
785C23C22×C22⋊D712yes—
786C23C24×D711yescharacteristic
787Q8—2816no—
788D4—416no—
789D4—1432no—
790D4—2816no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—148no—
814C2×C4—148no—
815C2×C4—148no—
816C2×C4—148no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—2816no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4C22×C22⋊D714yes—
839C2×C4C22×C22⋊D714yes—
840C2×C4C22×C22⋊D714yes—
841C7C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—416no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—144no—
859C22—144no—
860C22—144no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—2816no—
866C22#9034614yes—
867C22#9034714yes—
868C22#9035014yes—
869C22#9035314yes—
870C22D4×C22⋊D714yes—
871C22#9052214yes—
872C22#9052314yes—
873C22C22×D4×D711yescharacteristic
874C22C2×#654811yescharacteristic
875C22C2×D7×#4111yescharacteristic
876C22C2×D7×#4111yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×#655411yescharacteristic
879C22C23×C22⋊D711yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—144no—
886C4—144no—
887C4—144no—
888C4—144no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—82no—
894C2—284no—
895C2#1174029718yesdirect product factor
896C2C2×#9034711yescharacteristic
897C2C2×#9035311yescharacteristic
898C2C2×#9034611yescharacteristic
899C2C2×#9035011yescharacteristic
900C2C2×D4×C22⋊D711yescharacteristic
901C2C2×#9052311yescharacteristic
902C2C2×#9052211yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#123C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×#123D7
hypocenterC7C2×#2461
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C7×#123C2semidirect
2. C22×#6499C2semidirect
3. C22×C4×C22⋊D7C2semidirect
4. C22×#6459C2semidirect
6. C2×#89982C2semidirect
7. #11740297C2direct (N × H)
8. C2×#89751C2semidirect
9. C2×#89762C2semidirect
10. C2×C4⋊C4×Dic7C2semidirect
11. C2×#89728C2semidirect
12. C2×#89720C2semidirect
13. C2×#89733C2semidirect
14. C2×#89729C2semidirect
15. C2×#89717C2semidirect
16. C2×#89717C2semidirect
24. C2×C7×#123C22semidirect
37. C2×#6499C22semidirect
39. C2×C4×C22⋊D7C22semidirect
53. C2×#6459C22semidirect
55. #89982C22semidirect
62. #89762C22semidirect
63. #89751C22semidirect
64. C4⋊C4×Dic7C22semidirect
65. #89733C22semidirect
66. #89729C22semidirect
67. #89728C22semidirect
68. #89720C22semidirect
69. #89717C22semidirect
70. #89717C22semidirect
113. C2×C7×C4⋊C4D4semidirect
127. C2×C22⋊Dic7D4semidirect
168. C22×#123D7semidirect
281. C7×C4⋊C4C2×D4semidirect
290. C22⋊Dic7C2×D4semidirect
312. C2×#123C2×D7semidirect
515. C2×C4⋊C4C22⋊D7semidirect
709. C4⋊C4C2×C22⋊D7semidirect
728. C2×C7#2461semidirect
841. C7C2×#2461semidirect
895. C2#11740297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C22×#64992
C22×C4×C22⋊D72
C22×#64592
C2×#899952
C2×#899822
#117402972
C2×#897512
C2×#897622
C2×C4⋊C4×Dic72
C2×#897282
C2×#897202
C2×#897332
C2×#897292
C2×#897172
C2×#24617