Finite Group Databasebeta

← #13515085

Subgroups — #13515085

Order 1792.

2930 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90415C211yesmaximal, characteristic
2C2×#90263C211yesmaximal, characteristic, complemented
3C2×#90265C211yesmaximal, characteristic
4C7×#2327C211yesmaximal, characteristic, complemented
5Dic7×C4⋊Q8C211yesmaximal, characteristic, complemented
6C4×#6507C211yesmaximal, characteristic, complemented
7C4×#6510C211yesmaximal, characteristic, complemented
8D7×#391C211yesmaximal, characteristic, complemented
9#11733930C211yesmaximal, characteristic, complemented
10#11733929C211yesmaximal, characteristic, complemented
11#11733923C211yesmaximal, characteristic
12#11732753C214yesmaximal, complemented
13#11732752C214yesmaximal, complemented
14#11732411C214yesmaximal, complemented
15#11732410C214yesmaximal, complemented
16#11731670C211yesmaximal, characteristic, complemented
17#11731594C211yesmaximal, characteristic, complemented
18#11730832C211yesmaximal, characteristic, complemented
19#11730827C211yesmaximal, characteristic, complemented
20C22×#1161C2211yescharacteristic
21C22×Q8×D7C2211yescharacteristic
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C4×C7×Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×#6510C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C2×Q8×Dic7C2211yescharacteristic
28C2×#6507C2211yescharacteristic
29#90415C4116yescomplemented
30#90265—28no—
31#90263—28no—
32C2×#6459C2214yes—
33C2×#6457C2214yes—
34C2×#6456C2212yes—
35C2×#6456C2211yescharacteristic
36C2×#6455C2212yes—
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2212yes—
40C2×#6450C2211yescharacteristic
41C2×#6450C2212yes—
42C2×#6438C2211yescharacteristic
43C2×C4×D28C2212yes—
44C2×C4×D28C2211yescharacteristic
45C2×#6435C2212yes—
46C2×#6435C2212yes—
47C2×#6435C2211yescharacteristic
48C2×#6435C2211yescharacteristic
49C2×C42×D7C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C2×C4×Dic14C2212yes—
52C7×#391C2211yescharacteristic
53C7×#391C2211yescharacteristic
54C7×#387C2214yes—
55C7×#387C2214yes—
56C7×#382C2211yescharacteristic
57C7×#376C2211yescharacteristic
58#90002C2211yescharacteristic
59#90002C2211yescharacteristic
60#89762C2214yes—
61#89760C2211yescharacteristic
62#89757C2214yes—
63#89749C2211yescharacteristic
64#89748C2211yescharacteristic
65C4⋊C4×Dic7C2214yes—
66#89746C2211yescharacteristic
67#89744C2214yes—
68#89711C2211yescharacteristic
69C4×(C2×D7)⋊C4C2214yes—
70#89707C2211yescharacteristic
71#89704C2211yescharacteristic
72C4×Dic7⋊C4C2214yes—
73C42×Dic7C2211yescharacteristic
74C42×Dic7C2211yescharacteristic
75#89701C2211yescharacteristic
76#89442C2214yes—
77#89441C2214yes—
78#89441C2214yes—
79#89440C2214yes—
80#89440C2214yes—
81#89440C2214yes—
82#89438C2212yes—
83#89438C2212yes—
84#89438C2214yes—
85#89438C2214yes—
86#89437C2214yes—
87D7×#95C2214yes—
88#89427C2214yes—
89#89424C2214yes—
90#89421C2212yes—
91#89421C2212yes—
92#89419C2214yes—
93#89418C2214yes—
94#34276—71nomaximal, Sylow
95C22×C7×Q8C2311yescharacteristic
96C22×C7×Q8C2311yescharacteristic
97C2×#1161—24no—
98C2×#1161—24no—
99C2×#1161C2×C418yes—
100C2×Q8×D7—24no—
101C2×Q8×D7—24no—
102C2×Q8×D7C2×C418yescomplemented
103C22×D28C2311yescharacteristic
104C22×D28C2312yes—
105C22×C4×D7C2312yes—
106C22×C4×D7C2312yes—
107C22×C4×D7C2312yes—
108C22×C4×D7C2312yes—
109C22×C4×D7C2312yes—
110C22×C4×D7C2312yes—
111C22×C4×D7C2311yescharacteristic
112C22×Dic14C2311yescharacteristic
113C22×Dic14C2312yes—
114C7×C4⋊Q8C2×C418yescomplemented
115C4×C7×Q8—24no—
116C4×C7×Q8—24no—
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2312yes—
119C2×C7×C4⋊C4C2312yes—
120C2×C7×C4⋊C4C2311yescharacteristic
121C2×C7×C4⋊C4C2314yes—
122C2×C42×C7C2312yes—
123C2×C42×C7C2311yescharacteristic
124C2×C42×C7C2312yes—
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127#6510C2×C418yescomplemented
128Q8×Dic7—24no—
129Q8×Dic7—24no—
130#6507C2×C418yescomplemented
131C2×(C2×D7)⋊C4C2312yes—
132C2×(C2×D7)⋊C4C2312yes—
133C2×(C2×D7)⋊C4C2312yes—
134C2×(C2×D7)⋊C4C2314yes—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2312yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2311yescharacteristic
140C2×(C2×D7)⋊C4C2311yescharacteristic
141C2×C4⋊Dic7C2312yes—
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2312yes—
144C2×C4⋊Dic7C2311yescharacteristic
145C2×C4⋊Dic7C2314yes—
146C2×Dic7⋊C4C2312yes—
147C2×Dic7⋊C4C2312yes—
148C2×Dic7⋊C4C2312yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2312yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2311yescharacteristic
153C2×Dic7⋊C4C2311yescharacteristic
154C2×C4×Dic7C2312yes—
155C2×C4×Dic7C2312yes—
156C2×C4×Dic7C2312yes—
157C2×C4×Dic7C2312yes—
158C2×C4×Dic7C2311yescharacteristic
159C2×C4×Dic7C2312yes—
160C2×C4×Dic7C2312yes—
161C2×C4×Dic7C2312yes—
162C2×C4×Dic7C2312yes—
163C2×C4×Dic7C2312yes—
164C2×C4×Dic7C2312yes—
165C2×C4×Dic7C2311yescharacteristic
166C2×C4×Dic7C2311yescharacteristic
167#6459C2×C4132yescomplemented
168#6457C2×C4132yescomplemented
169#6456—28no—
170#6456—24no—
171#6455—24no—
172#6455—28no—
173D7×C4⋊C4—24no—
174D7×C4⋊C4—28no—
175#6450—28no—
176#6450—24no—
177#6438C2×C418yescomplemented
178C4×D28—24no—
179C4×D28—28no—
180#6435—28no—
181#6435—28no—
182#6435C2×C418yescomplemented
183#6435D418yes—
184C42×D7—24no—
185C4×Dic14—24no—
186C4×Dic14—28no—
187C7×#95C2314yes—
188C7×#95C2314yes—
189C7×#95C2312yes—
190C7×#95C2312yes—
191C7×#95C2314yes—
192C7⋊#95C2314yes—
193C7⋊#95C2314yes—
194C7⋊#95C2314yes—
195C7⋊#95C2314yes—
196C7⋊#95C2312yes—
197C7⋊#95C2312yes—
198C7⋊#95C2314yes—
199C2×#536—71no—
200C2×#520—71no—
201C2×#519—71no—
202#2362—74no—
203#2360—74no—
204#2359—74no—
205#2359—74no—
206#2327—71no—
207#2327D711yescharacteristic, complemented
208#2326—71no—
209#2326—71no—
210#2317—71no—
211C4×C4⋊Q8—71no—
212C4×C4⋊Q8—71no—
213C4×#124—71no—
214C4×#124—71no—
215#2297—71no—
216C2×#391—71no—
217C4×#117—71no—
218C23×D7C2412yes—
219C23×D7C2411yescharacteristic
220C2×C7×Q8—22no—
221C2×C7×Q8—22no—
222C2×C7×Q8—22no—
223C2×C7×Q8—22no—
224C2×C7×Q8C22×C414yes—
225C2×C7×Q8C22×C414yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2411yescharacteristic
233C22×C4×C7C2411yescharacteristic
234C22×C4×C7C2411yescharacteristic
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C22×Dic7C2412yes—
239C22×Dic7C2411yescharacteristic
240C22×Dic7C2411yescharacteristic
241C22×Dic7C2412yes—
242C22×Dic7C2411yescharacteristic
243#1161—232no—
244Q8×D7—232no—
245C2×D28—24no—
246C2×D28—24no—
247C2×D28—22no—
248C2×D28—22no—
249C2×D28C22×C414yes—
250C2×D28C22×C418yes—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—24no—
254C2×C4×D7—24no—
255C2×C4×D7—24no—
256C2×C4×D7—24no—
257C2×C4×D7—24no—
258C2×C4×D7—24no—
259C2×C4×D7—24no—
260C2×C4×D7—42no—
261C2×C4×D7—44no—
262C2×C4×D7—44no—
263C2×C4×D7—44no—
264C2×C4×D7C22×C418yes—
265C2×C4×D7C22×C418yes—
266C2×C4×D7C22×C414yes—
267C2×C4×D7C2×D414yes—
268C2×C4×D7#4114yes—
269C2×Dic14—22no—
270C2×Dic14—22no—
271C2×Dic14—24no—
272C2×Dic14—24no—
273C2×Dic14C22×C414yes—
274C2×Dic14C22×C418yes—
275C7×C4⋊C4—24no—
276C7×C4⋊C4—22no—
277C7×C4⋊C4—24no—
278C7×C4⋊C4—22no—
279C7×C4⋊C4C22×C4116yes—
280C42×C7—24no—
281C42×C7—24no—
282C42×C7—22no—
283C42×C7C22×C414yes—
284C42×C7C2×D414yes—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287(C2×D7)⋊C4—24no—
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—44no—
290(C2×D7)⋊C4C22×C418yes—
291(C2×D7)⋊C4C22×C4116yes—
292(C2×D7)⋊C4C22×C4116yes—
293(C2×D7)⋊C4C2×D414yes—
294(C2×D7)⋊C4C2×D414yes—
295C4⋊Dic7—22no—
296C4⋊Dic7—22no—
297C4⋊Dic7—24no—
298C4⋊Dic7—24no—
299C4⋊Dic7—44no—
300Dic7⋊C4—24no—
301Dic7⋊C4—24no—
302Dic7⋊C4—24no—
303Dic7⋊C4—44no—
304Dic7⋊C4C22×C418yes—
305Dic7⋊C4C22×C4116yes—
306Dic7⋊C4C2×D414yes—
307Dic7⋊C4C2×D414yes—
308C4×Dic7—24no—
309C4×Dic7—22no—
310C4×Dic7—24no—
311C4×Dic7—24no—
312C4×Dic7—24no—
313C4×Dic7—24no—
314C4×Dic7—24no—
315C4×Dic7—24no—
316C4×Dic7—24no—
317C4×Dic7—42no—
318C4×Dic7—42no—
319C4×Dic7C22×C414yes—
320C4×Dic7C2×D414yes—
321C22×#41—71no—
322C23×Q8—71no—
323#536—716no—
324C2×C4⋊Q8—71no—
325C2×C4⋊Q8C2×D711yescharacteristic
326C2×#124—71no—
327C2×#124—71no—
328C2×#123—74no—
329C2×C22⋊Q8—74no—
330#520—148no—
331#519—148no—
332C2×C4×Q8—71no—
333C2×C4×Q8—71no—
334C2×C4×Q8—71no—
335C2×C4×Q8—72no—
336C2×C4×Q8—71no—
337C2×C4×Q8—72no—
338C2×C4×Q8C2×D711yescharacteristic
339C2×C4×Q8C2×D711yescharacteristic
340C2×C4×D4—71no—
341C2×C4×D4—72no—
342C2×C4×D4—71no—
343C2×C4×D4—72no—
344C2×#117—71no—
345C2×#117—72no—
346C2×#117—71no—
347C2×#117—71no—
348C2×#117—72no—
349C2×#117—72no—
350C22×C4⋊C4—71no—
351C22×C4⋊C4—72no—
352C22×C42—71no—
353#391—71no—
354#391—71no—
355#391—71no—
356#391—71no—
357#391—74no—
358#391C2×D711yescharacteristic
359#391C2×D711yescharacteristic
360#390—71no—
361#390—71no—
362#389—74no—
363#389—74no—
364#389—74no—
365#388—74no—
366#388—74no—
367#388—74no—
368#388—74no—
369#387—74no—
370#387—74no—
371#387C2×D714yes—
372#387C2×D714yes—
373#386—74no—
374#385—74no—
375#385—74no—
376#385—74no—
377#384—71no—
378#384—71no—
379#382—71no—
380#382C2×D711yescharacteristic
381C4×C4⋊C4—74no—
382C4×C4⋊C4—74no—
383C4×C4⋊C4—72no—
384C4×C4⋊C4—72no—
385C4×C22⋊C4—74no—
386C4×C22⋊C4—72no—
387C4×C22⋊C4—72no—
388C4×C22⋊C4—74no—
389C4×C22⋊C4—74no—
390#376—71no—
391#376C2×D711yescharacteristic
392C2×#95—74no—
393C43—71no—
394C43—71no—
395C23×C7C2511yescharacteristic
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—24no—
401C22×D7—24no—
402C22×D7C23×C414yes—
403C22×D7C23×C412yes—
404C22×D7C22×D412yes—
405C22×D7C2×#4112yes—
406C7×Q8—28no—
407C7×Q8—28no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
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—24no—
420C2×C4×C7—22no—
421C2×C4×C7—24no—
422C2×C4×C7—22no—
423C2×C4×C7C23×C414yes—
424C2×C4×C7C23×C414yes—
425C2×C4×C7C23×C414yes—
426C2×C4×C7C23×C412yes—
427C2×C4×C7C22×D412yes—
428C2×C4×C7C22×D412yes—
429C2×C4×C7C22×D412yes—
430C2×C4×C7C2×#4112yes—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—24no—
442C2×Dic7—24no—
443C2×Dic7C23×C414yes—
444C2×Dic7C23×C414yes—
445C2×Dic7C23×C412yes—
446C2×Dic7C22×D412yes—
447C2×Dic7C22×D412yes—
448C2×Dic7C22×D412yes—
449C2×Dic7C2×#4112yes—
450C2×Dic72−1+414yes—
451D28—216no—
452D28—28no—
453C4×D7—216no—
454C4×D7—216no—
455C4×D7—48no—
456C4×D7—84no—
457C4×D7—84no—
458C4×D7—84no—
459C4×D7C4×D4116yes—
460Dic14—28no—
461Dic14—216no—
462C2×#41—78no—
463C2×#41—144no—
464C2×#41—144no—
465C22×Q8—78no—
466C22×Q8—72no—
467C22×Q8—71no—
468C22×Q8—144no—
469C22×Q8—144no—
470C22×Q8C22×D711yescharacteristic
471C22×Q8C22×D711yescharacteristic
472C22×D4—72no—
473C22×D4—71no—
474C23×C4—71no—
475C23×C4—72no—
476C23×C4—72no—
477C23×C4—72no—
478C23×C4—72no—
479C23×C4—72no—
480C23×C4—72no—
481C4⋊Q8—78no—
482C4⋊Q8C4×D718yescomplemented
483#124—78no—
484#124—78no—
485#123—732no—
486C22⋊Q8—732no—
487C4×Q8—24no—
488C4×Q8—24no—
489C4×Q8—148no—
490C4×Q8—144no—
491C4×Q8—144no—
492C4×Q8—144no—
493C4×Q8—148no—
494C4×Q8—144no—
495C4×D4—148no—
496C4×D4—144no—
497C4×D4—148no—
498C4×D4—144no—
499#117—78no—
500#117—78no—
501#117—148no—
502#117—148no—
503#117—148no—
504#117—144no—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—72no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—72no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4—74no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—148no—
519C2×C4⋊C4—144no—
520C2×C4⋊C4C22×D711yescharacteristic
521C2×C4⋊C4C22×D712yes—
522C2×C4⋊C4C22×D711yescharacteristic
523C2×C4⋊C4C22×D712yes—
524C2×C4⋊C4C22×D714yes—
525C2×C22⋊C4—71no—
526C2×C22⋊C4—71no—
527C2×C22⋊C4—72no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—72no—
531C2×C22⋊C4—72no—
532C2×C22⋊C4—72no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C42—71no—
536C2×C42—71no—
537C2×C42—72no—
538C2×C42—72no—
539C2×C42—72no—
540C2×C42—72no—
541C2×C42—72no—
542C2×C42—71no—
543C2×C42—72no—
544C2×C42—72no—
545C2×C42—72no—
546C2×C42—72no—
547C2×C42—72no—
548C2×C42—144no—
549C2×C42C22×D712yes—
550C2×C42C22×D712yes—
551C2×C42C22×D711yescharacteristic
552C2×C42C22×D711yescharacteristic
553C2×C42C22×D711yescharacteristic
554#95—74no—
555#95—74no—
556#95—74no—
557#95—72no—
558#95—72no—
559#95—74no—
560#95—74no—
561#95C22×D714yes—
562#95C22×D712yes—
563#95C22×D712yes—
564#95C22×D714yes—
565#95C22×D714yes—
566C22×C7C24×C411yescharacteristic
567C22×C7C23×D411yescharacteristic
568C22×C7C22×#4111yescharacteristic
569C22×C7C2×2−1+412yes—
570C22×C7#58512yes—
571C2×D7—24no—
572C2×D7—24no—
573C2×D7—22no—
574C2×D7—22no—
575C2×D7—24no—
576C2×D7—28no—
577C2×D7—44no—
578C2×D7—42no—
579C2×D7—42no—
580C2×D7C2×C4×D414yes—
581C4×C7—24no—
582C4×C7—24no—
583C4×C7—24no—
584C4×C7—22no—
585C4×C7—22no—
586C4×C7—42no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7C2×C4×D414yes—
590Dic7—24no—
591Dic7—24no—
592Dic7—24no—
593Dic7—22no—
594Dic7—22no—
595Dic7—42no—
596Dic7—42no—
597Dic7C2×C4×D414yes—
598C24—71no—
599C24—72no—
600#41—1432no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—78no—
606C2×Q8—74no—
607C2×Q8—144no—
608C2×Q8—144no—
609C2×Q8—1432no—
610C2×Q8—142no—
611C2×Q8—142no—
612C2×Q8C2×C4×D714yes—
613C2×Q8C2×C4×D714yes—
614C2×D4—78no—
615C2×D4—74no—
616C2×D4—144no—
617C2×D4—144no—
618C2×D4—142no—
619C2×D4—142no—
620C22×C4—71no—
621C22×C4—74no—
622C22×C4—74no—
623C22×C4—74no—
624C22×C4—72no—
625C22×C4—72no—
626C22×C4—72no—
627C22×C4—71no—
628C22×C4—71no—
629C22×C4—78no—
630C22×C4—78no—
631C22×C4—72no—
632C22×C4—72no—
633C22×C4—144no—
634C22×C4—144no—
635C22×C4—144no—
636C22×C4—144no—
637C22×C4—144no—
638C22×C4—144no—
639C22×C4—144no—
640C22×C4—144no—
641C22×C4—144no—
642C22×C4—282no—
643C22×C4—284no—
644C22×C4—284no—
645C22×C4—284no—
646C22×C4C23×D712yes—
647C22×C4C23×D712yes—
648C22×C4C23×D712yes—
649C22×C4C23×D712yes—
650C22×C4C23×D712yes—
651C22×C4C23×D712yes—
652C22×C4C23×D711yescharacteristic
653C22×C4C23×D711yescharacteristic
654C22×C4C23×D711yescharacteristic
655C4⋊C4—24no—
656C4⋊C4—22no—
657C4⋊C4—24no—
658C4⋊C4—22no—
659C4⋊C4—78no—
660C4⋊C4—716no—
661C4⋊C4—74no—
662C4⋊C4—74no—
663C4⋊C4—144no—
664C4⋊C4—144no—
665C4⋊C4—144no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—142no—
669C4⋊C4—142no—
670C4⋊C4—284no—
671C4⋊C4—284no—
672C4⋊C4C2×C4×D7116yes—
673C22⋊C4—78no—
674C22⋊C4—716no—
675C22⋊C4—716no—
676C22⋊C4—74no—
677C22⋊C4—74no—
678C22⋊C4—148no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4—284no—
683C42—24no—
684C42—24no—
685C42—22no—
686C42—74no—
687C42—74no—
688C42—144no—
689C42—144no—
690C42—144no—
691C42—144no—
692C42—144no—
693C42—144no—
694C42—144no—
695C42—144no—
696C42—142no—
697C42—282no—
698C42—282no—
699C42C2×C4×D714yes—
700C42D4×D714yes—
701C2×C7C22×C4×D411yescharacteristic
702C2×C7C4×2−1+412yes—
703C2×C7#349512yes—
704C2×C7#349911yescharacteristic
705C2×C7#350011yescharacteristic
706D7—24no—
707D7—44no—
708C23—72no—
709C23—72no—
710C23—72no—
711C23—74no—
712C23—142no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—144no—
717C23—144no—
718C23C24×D711yescharacteristic
719Q8—28no—
720Q8—28no—
721Q8—1416no—
722Q8—148no—
723D4—1416no—
724D4—148no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—72no—
741C2×C4—72no—
742C2×C4—72no—
743C2×C4—716no—
744C2×C4—74no—
745C2×C4—74no—
746C2×C4—72no—
747C2×C4—72no—
748C2×C4—74no—
749C2×C4—1416no—
750C2×C4—1416no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—142no—
757C2×C4—142no—
758C2×C4—142no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—144no—
762C2×C4—144no—
763C2×C4—288no—
764C2×C4—564no—
765C2×C4—564no—
766C2×C4—564no—
767C2×C4C22×C4×D714yes—
768C2×C4C22×C4×D714yes—
769C2×C4C22×C4×D714yes—
770C2×C4C22×C4×D712yes—
771C2×C4C2×D4×D712yes—
772C2×C4C2×D4×D712yes—
773C2×C4C2×D4×D712yes—
774C2×C4D7×#4112yes—
775C7#3427611yescharacteristic, complemented, Sylow
776C22—74no—
777C22—144no—
778C22—142no—
779C22—142no—
780C22—144no—
781C22—144no—
782C22—148no—
783C22—284no—
784C22—282no—
785C22—282no—
786C22C23×C4×D711yescharacteristic
787C22C22×D4×D711yescharacteristic
788C22C2×D7×#4111yescharacteristic
789C22D7×2−1+412yes—
790C22#9062012yes—
791C4—24no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—24no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—74no—
800C4—144no—
801C4—144no—
802C4—142no—
803C4—142no—
804C4—144no—
805C4—282no—
806C4—282no—
807C4C4×D4×D714yes—
808C2—144no—
809C2—284no—
810C2C2×C4×D4×D711yescharacteristic
811C2#1174294112yes—
812C2#1174340811yescharacteristic
813C2#1174340911yescharacteristic
814C2#1174357712yes—
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC7×#2327C2
socle, cosocleC23×C7C25
prime radicalC22×#1161C22
hypercenter#2327D7
hypocenterC7#34276
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. C2×#90263C2semidirect
4. C7×#2327C2semidirect
5. Dic7×C4⋊Q8C2semidirect
6. C4×#6507C2semidirect
7. C4×#6510C2semidirect
8. D7×#391C2semidirect
9. #11733930C2semidirect
10. #11733929C2semidirect
12. #11732753C2semidirect
13. #11732752C2semidirect
14. #11732411C2semidirect
15. #11732410C2semidirect
16. #11731670C2semidirect
17. #11731594C2semidirect
18. #11730832C2semidirect
19. #11730827C2semidirect
29. #90415C4semidirect
102. C2×Q8×D7C2×C4semidirect
114. C7×C4⋊Q8C2×C4semidirect
127. #6510C2×C4semidirect
130. #6507C2×C4semidirect
167. #6459C2×C4semidirect
168. #6457C2×C4semidirect
177. #6438C2×C4semidirect
182. #6435C2×C4semidirect
207. #2327D7semidirect
482. C4⋊Q8C4×D7semidirect
775. C7#34276semidirect

Maximal subgroups

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

subgroupindex
C2×#904152
C2×#902632
C2×#902652
C7×#23272
Dic7×C4⋊Q82
C4×#65072
C4×#65102
D7×#3912
#117339302
#117339292
#117339232
#117327532
#117327522
#117324112
#117324102
#117316702
#117315942
#117308322
#117308272
#342767