Finite Group Databasebeta

← C2×#11739855 #13521293

Subgroups — C2×#11739855 #13521293

Order 1792.

3894 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×C4×C7×D4C211yesmaximal, characteristic, complemented
2C22×#6492C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D7C211yesmaximal, characteristic, complemented
4C22×#6446C211yesmaximal, characteristic, complemented
5C2×#89995C211yesmaximal, characteristic
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89982C211yesmaximal, characteristic, complemented
8C2×#89982C211yesmaximal, characteristic, complemented
9#11739855C2116yesmaximal, direct product factor
10C2×#89761C211yesmaximal, characteristic, complemented
11C2×#89744C211yesmaximal, characteristic, complemented
12C2×#89721C211yesmaximal, characteristic, complemented
13C2×#89733C211yesmaximal, characteristic, complemented
14C2×#89723C211yesmaximal, characteristic, complemented
15C2×#89700C211yesmaximal, characteristic, complemented
16C2×#89712C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C24×C4×C7C2211yescharacteristic
20C23×C22⋊D7C2211yescharacteristic
21C23×C22⋊D7C2211yescharacteristic
22C23×C4×D7C2211yescharacteristic
23C2×C4×C7×D4—28no—
24C2×C4×C7×D4C2218yescomplemented
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C22×C22⋊Dic7C2211yescharacteristic
34C22×C22⋊Dic7C2211yescharacteristic
35C2×#6492—28no—
36C2×#6492C2218yescomplemented
37C2×C4×C22⋊D7—28no—
38C2×C4×C22⋊D7C2218yescomplemented
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×(C2×D7)⋊C4C2211yescharacteristic
43C22×C4⋊Dic7C2211yescharacteristic
44C22×C4⋊Dic7C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×Dic7⋊C4C2211yescharacteristic
48C22×Dic7⋊C4C2211yescharacteristic
49C22×Dic7⋊C4C2211yescharacteristic
50C22×Dic7⋊C4C2211yescharacteristic
51C22×C4×Dic7C2211yescharacteristic
52C2×#6446—28no—
53C2×#6446C2218yescomplemented
54#89995C2218yes—
55#89994C2218yescomplemented
56#89982C2218yescomplemented
57#89982C2218yescomplemented
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62C2×C7⋊#95C2211yescharacteristic
63C2×C7⋊#95C2211yescharacteristic
64#89761C2218yescomplemented
65#89744C2218yescomplemented
66#89733C2218yescomplemented
67#89723C2218yescomplemented
68#89721C2218yescomplemented
69#89712C2218yescomplemented
70#89700C2218yescomplemented
71C2×#2455—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—24no—
78C22×C7×D4C2314yes—
79C23×C4×C7—24no—
80C23×C4×C7—24no—
81C23×C4×C7—24no—
82C23×C4×C7—24no—
83C23×C4×C7—42no—
84C23×C4×C7—42no—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2314yes—
87C23×C4×C7C2314yes—
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C22×C22⋊D7—24no—
93C22×C22⋊D7—24no—
94C22×C22⋊D7—24no—
95C22×C22⋊D7—24no—
96C22×C22⋊D7—24no—
97C22×C22⋊D7—42no—
98C22×C22⋊D7C2314yes—
99C22×C22⋊D7C2314yes—
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C23×Dic7C2311yescharacteristic
104C23×Dic7C2311yescharacteristic
105C23×Dic7C2311yescharacteristic
106C23×Dic7C2311yescharacteristic
107C22×C4×D7—24no—
108C22×C4×D7—24no—
109C22×C4×D7—42no—
110C22×C4×D7C2314yes—
111C4×C7×D4—232no—
112C2×C7×C4⋊C4—24no—
113C2×C7×C4⋊C4C2314yes—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4D418yescomplemented
116C2×C7×C22⋊C4C2314yes—
117C2×C7×C22⋊C4C2314yes—
118C2×C42×C7—24no—
119C2×C42×C7C2314yes—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7—42no—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131C2×C22⋊Dic7C2314yes—
132#6492—232no—
133C4×C22⋊D7—232no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4D418yescomplemented
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×C4⋊Dic7—24no—
143C2×C4⋊Dic7—24no—
144C2×C4⋊Dic7C2314yes—
145C2×C4⋊Dic7C2314yes—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—24no—
148C2×Dic7⋊C4—24no—
149C2×Dic7⋊C4—24no—
150C2×Dic7⋊C4—24no—
151C2×Dic7⋊C4—42no—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×Dic7⋊C4C2314yes—
155C2×Dic7⋊C4C2314yes—
156C2×Dic7⋊C4C2314yes—
157C2×Dic7⋊C4C2314yes—
158C2×C4×Dic7—24no—
159C2×C4×Dic7C2314yes—
160#6446—232no—
161C7⋊#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#123—71no—
168C22×#123—71no—
169C22×C4×D4—71no—
170C22×C4×D4D711yescharacteristic, complemented
171#2455—716no—
172C2×#399—71no—
173C2×#394—71no—
174C2×#394—71no—
175C2×#392—71no—
176C2×#389—71no—
177C2×#389—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#385—71no—
181C2×#385—71no—
182C2×#385—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×C7C2×D414yes—
196C24×C7#4114yes—
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×D7C2×D414yes—
207C23×D7C2412yes—
208C2×C7×D4—232no—
209C2×C7×D4—28no—
210C2×C7×D4—28no—
211C2×C7×D4—28no—
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—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—28no—
223C22×C4×C7—22no—
224C22×C4×C7—28no—
225C22×C4×C7—28no—
226C22×C4×C7—28no—
227C22×C4×C7—44no—
228C22×C4×C7—44no—
229C22×C4×C7—416no—
230C22×C4×C7—416no—
231C22×C4×C7C2×D414yes—
232C22×C4×C7C2×D414yes—
233C22×C4×C7C2×D414yes—
234C22×C4×C7#4114yes—
235C22×C4×C7C2412yes—
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2412yes—
239C22×C4×C7C2412yes—
240C2×C22⋊D7—232no—
241C2×C22⋊D7—28no—
242C2×C22⋊D7—28no—
243C2×C22⋊D7—28no—
244C2×C22⋊D7—28no—
245C2×C22⋊D7—28no—
246C2×C22⋊D7—44no—
247C2×C22⋊D7—416no—
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×Dic7—22no—
262C22×Dic7—22no—
263C22×Dic7—22no—
264C22×Dic7—22no—
265C22×Dic7—22no—
266C22×Dic7—22no—
267C22×Dic7C2×D414yes—
268C22×Dic7#4114yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C22×Dic7C2412yes—
273C22×Dic7C2412yes—
274C22×Dic7C2412yes—
275C22×Dic7C2412yes—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—44no—
279C2×C4×D7—416no—
280C7×C4⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4C2×D4116yescomplemented
283C42×C7—28no—
284C22⋊Dic7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7—44no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4C2×D4116yescomplemented
294C4⋊Dic7—28no—
295C4⋊Dic7—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301Dic7⋊C4—44no—
302C4×Dic7—28no—
303C23×D4—71no—
304C23×D4—71no—
305C23×D4C2×D711yescharacteristic
306C24×C4—71no—
307C24×C4C2×D711yescharacteristic
308C24×C4C2×D711yescharacteristic
309C2×#123—78no—
310C2×#123—78no—
311C2×#123—148no—
312C2×#123—148no—
313C2×C4×D4—28no—
314C2×C4×D4—78no—
315C2×C4×D4—148no—
316C2×C4×D4C2×D718yescomplemented
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4C2×D711yescharacteristic
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⋊C4—71no—
335C22×C22⋊C4—71no—
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C22⋊C4C2×D711yescharacteristic
338C22×C42—71no—
339C22×C42C2×D711yescharacteristic
340#399—78no—
341#394—78no—
342#394—78no—
343#392—78no—
344#389—78no—
345#389—78no—
346#388—78no—
347#388—78no—
348#385—78no—
349#385—78no—
350#385—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—28no—
361C23×C7—28no—
362C23×C7—28no—
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—22no—
374C23×C7—22no—
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×C7C22×D412yes—
384C23×C7C22×D414yes—
385C23×C7C22×D412yes—
386C23×C7C2×#4114yes—
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×D7C22×D414yes—
407C7×D4—232no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—28no—
411C2×C4×C7—28no—
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—416no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C22×D414yes—
428C2×C4×C7C22×D414yes—
429C2×C4×C7C2×#4114yes—
430C22⋊D7—232no—
431C22⋊D7—416no—
432C2×Dic7—28no—
433C2×Dic7—28no—
434C2×Dic7—22no—
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—22no—
453C2×Dic7—44no—
454C2×Dic7—44no—
455C2×Dic7—44no—
456C2×Dic7—44no—
457C2×Dic7—44no—
458C2×Dic7C22×D414yes—
459C2×Dic7C2×#4114yes—
460C4×D7—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—74no—
468C22×D4—74no—
469C22×D4—144no—
470C22×D4—144no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—282no—
475C22×D4C22×D714yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—42no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—74no—
490C23×C4—144no—
491C23×C4—144no—
492C23×C4—282no—
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D714yes—
495C23×C4C22×D714yes—
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500#123—1432no—
501#123—1432no—
502C4×D4—232no—
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—74no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—144no—
514C2×C4⋊C4—144no—
515C2×C4⋊C4—144no—
516C2×C4⋊C4—144no—
517C2×C4⋊C4—144no—
518C2×C4⋊C4—144no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4—282no—
521C2×C4⋊C4C22×D714yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—78no—
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—74no—
533C2×C22⋊C4—74no—
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⋊C4—144no—
542C2×C22⋊C4—282no—
543C2×C22⋊C4C22⋊D718yescomplemented
544C2×C22⋊C4C22×D714yes—
545C2×C22⋊C4C22×D714yes—
546C2×C42—24no—
547C2×C42—74no—
548C2×C42—144no—
549C2×C42C22×D714yes—
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—24no—
560C22×C7—24no—
561C22×C7—24no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—416no—
569C22×C7—416no—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7#52514yes—
573C22×C7#52514yes—
574C22×C7#53914yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54714yes—
578C22×C7#55914yes—
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—416no—
593C2×D7—42no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—24no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—42no—
602Dic7—42no—
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—74no—
619C24—72no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24#115714yes—
627C24C2×C22⋊D714yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×D4—232no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—148no—
636C2×D4—148no—
637C2×D4—1432no—
638C2×D4—148no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—284no—
642C2×D4—2816no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
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—28no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—416no—
661C22×C4—416no—
662C22×C4—74no—
663C22×C4—74no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—72no—
670C22×C4—72no—
671C22×C4—148no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
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—148no—
692C22×C4—284no—
693C22×C4—2816no—
694C22×C4#115714yes—
695C22×C4D4×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—148no—
709C4⋊C4—148no—
710C4⋊C4—148no—
711C4⋊C4—284no—
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—284no—
723C22⋊C4C2×C22⋊D7116yescomplemented
724C42—28no—
725C42—148no—
726C2×C7—44no—
727C2×C7—44no—
728C2×C7#245518yescomplemented
729C2×C7C2×#52511yescharacteristic
730C2×C7C2×#52511yescharacteristic
731C2×C7C2×#53911yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54711yescharacteristic
735C2×C7C2×#55911yescharacteristic
736D7—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—74no—
764C23—148no—
765C23—148no—
766C23—148no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—142no—
772C23—142no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23C2×#115714yes—
778C23C2×#115712yes—
779C23C2×#115712yes—
780C23C2×D4×D712yes—
781C23#654812yes—
782C23D7×#4112yes—
783C23#655412yes—
784C23C22×C22⋊D714yes—
785C23C22×C22⋊D712yes—
786C23C24×D711yescharacteristic
787D4—232no—
788D4—1432no—
789D4—2816no—
790C2×C4—28no—
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—416no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—148no—
811C2×C4—148no—
812C2×C4—142no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
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—2816no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4—284no—
835C2×C4—284no—
836C2×C4—284no—
837C2×C4C2×#115714yes—
838C2×C4C2×D4×D714yes—
839C2×C4C22×C22⋊D714yes—
840C2×C4C22×C22⋊D714yes—
841C7C2×#245511yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—144no—
859C22—144no—
860C22—144no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—2816no—
866C22#9023814yes—
867C22#9024214yes—
868C22#9025014yes—
869C22#9025514yes—
870C22#9048214yes—
871C22D4×C22⋊D714yes—
872C22#9051514yes—
873C22C22×#115711yescharacteristic
874C22C22×#115711yescharacteristic
875C22C22×D4×D711yescharacteristic
876C22C2×#654811yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×#655411yescharacteristic
879C22C23×C22⋊D711yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—144no—
886C4—144no—
887C4—282no—
888C4—282no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—44no—
894C2—284no—
895C2#1173985518yesdirect product factor
896C2C2×#9025511yescharacteristic
897C2C2×#9025011yescharacteristic
898C2C2×#9023811yescharacteristic
899C2C2×#9024211yescharacteristic
900C2C2×#9048211yescharacteristic
901C2C2×D4×C22⋊D711yescharacteristic
902C2C2×#9051511yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC2×#89995C2
hypercenterC22×C4×D4D7
hypocenterC7C2×#2455
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C7×D4C2semidirect
2. C22×#6492C2semidirect
3. C22×C4×C22⋊D7C2semidirect
4. C22×#6446C2semidirect
6. C2×#89994C2semidirect
7. C2×#89982C2semidirect
8. C2×#89982C2semidirect
9. #11739855C2direct (N × H)
10. C2×#89761C2semidirect
11. C2×#89744C2semidirect
12. C2×#89721C2semidirect
13. C2×#89733C2semidirect
14. C2×#89723C2semidirect
15. C2×#89700C2semidirect
16. C2×#89712C2semidirect
24. C2×C4×C7×D4C22semidirect
36. C2×#6492C22semidirect
38. C2×C4×C22⋊D7C22semidirect
53. C2×#6446C22semidirect
55. #89994C22semidirect
56. #89982C22semidirect
57. #89982C22semidirect
64. #89761C22semidirect
65. #89744C22semidirect
66. #89733C22semidirect
67. #89723C22semidirect
68. #89721C22semidirect
69. #89712C22semidirect
70. #89700C22semidirect
115. C2×C7×C22⋊C4D4semidirect
137. C2×(C2×D7)⋊C4D4semidirect
170. C22×C4×D4D7semidirect
282. C7×C22⋊C4C2×D4semidirect
293. (C2×D7)⋊C4C2×D4semidirect
316. C2×C4×D4C2×D7semidirect
543. C2×C22⋊C4C22⋊D7semidirect
723. C22⋊C4C2×C22⋊D7semidirect
728. C2×C7#2455semidirect
841. C7C2×#2455semidirect
895. C2#11739855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C22×#64922
C22×C4×C22⋊D72
C22×#64462
C2×#899952
C2×#899942
C2×#899822
#117398552
C2×#897612
C2×#897442
C2×#897212
C2×#897332
C2×#897232
C2×#897002
C2×#897122
C2×#24557