Subgroups — C 2 × #13090646 #72243928

maximal, direct product factor

C₂

yes

C₂×#10624556

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₉×C₃⋊D₃

—

C₂×C₃×#4181

C₃

yes

maximal, characteristic

C₂×C₃×D₉⋊C₉

—

C₂×C₃×D₉⋊C₉

—

C₂×C₃×D₉⋊C₉

—

#10624556

C₂²

yes

characteristic, complemented, Sylow

C₂×C₃³×C₉

D₃

yes

C₃×C₉×C₃⋊D₃

—

C₂×C₃×C₉⋊C₉

D₃

yes

C₂×C₃×C₉⋊C₉

D₃

yes

C₂×C₃×C₉⋊C₉

D₃

yes

C₂×C₃×C₃²⋊C₉

—

C₂×C₃×C₃²⋊C₉

C₂×C₃

yes

C₃×#4181

C₂×C₃

yes

—

C₃×D₉⋊C₉

—

C₃×D₉⋊C₉

—

C₃×D₉⋊C₉

—

C₂×#6855

—

C₂×#6855

—

C₂×#6855

—

C₂×C₃²×C₃⋊D₃

—

C₂×C₉×C₃⋊D₃

—

C₂×C₉×C₃⋊D₃

—

C₂×C₉×C₃⋊D₃

—

C₂×C₃×D₃×C₉

—

C₂×C₃×D₃×C₉

—

C₂×C₃×D₃×C₉

—

C₂×C₃×D₃×C₉

—

C₂×C₃²×D₉

—

C₂×C₃²×D₉

—

C₂×C₃²×D₉

—

C₂×#4181

C₉

yes

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₂×D₉⋊C₉

—

C₃³×C₉

C₂×D₃

yes

C₃×C₉⋊C₉

C₂×D₃

yes

C₃×C₉⋊C₉

C₂×D₃

yes

C₃×C₉⋊C₉

C₂×D₃

yes

C₃×C₃²⋊C₉

—

C₃×C₃²⋊C₉

C₂²×C₃

yes

—

—

—

C₂×C₃⁴

C₃×D₃

yes

C₃²×C₃⋊D₃

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

—

C₂×C₃²×C₉

C₃×D₃

yes

C₂×C₃²×C₉

C₃×D₃

yes

C₂×C₃²×C₉

C₃×D₃

yes

C₂×C₃²×C₉

C₃⋊D₃

yes

C₉×C₃⋊D₃

—

C₉×C₃⋊D₃

—

C₉×C₃⋊D₃

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃×D₃×C₉

—

C₃²×D₉

—

C₃²×D₉

—

C₃²×D₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

—

C₂×C₃²⋊C₉

C₂×C₉

yes

#4181

C₂×C₉

yes

complemented

100

D₉⋊C₉

—

101

D₉⋊C₉

—

102

D₉⋊C₉

—

103

D₉⋊C₉

—

104

D₉⋊C₉

—

105

D₉⋊C₉

—

106

D₉⋊C₉

—

107

D₉⋊C₉

—

108

D₉⋊C₉

—

109

C₂×C₃×C₃⋊D₃

—

110

C₂×C₃×C₃⋊D₃

—

111

C₂×C₃×C₃⋊D₃

—

112

C₂×C₃×C₃⋊D₃

—

113

C₂×C₃²×D₃

—

114

C₂×C₃²×D₃

—

115

C₂×C₃²×D₃

—

116

C₂×C₃²×D₃

—

117

C₂²×C₃×C₉

—

118

C₂×D₃×C₉

—

119

C₂×D₃×C₉

—

120

C₂×D₃×C₉

—

121

C₂×D₃×C₉

—

122

C₂×D₃×C₉

—

123

C₂×D₃×C₉

—

124

C₂×D₃×C₉

—

125

C₂×D₃×C₉

—

126

C₂×D₃×C₉

—

127

C₂×D₃×C₉

—

128

C₂×D₃×C₉

—

129

C₂×D₃×C₉

—

130

C₂×C₃×D₉

—

131

C₂×C₃×D₉

—

132

C₂×C₃×D₉

—

133

C₂×C₃×D₉

—

134

C₂×C₃×D₉

—

135

C₂×C₃×D₉

—

136

C₂×C₃×D₉

—

137

C₂×C₃×D₉

—

138

C₂×C₃×D₉

—

139

C₂×C₃×D₉

—

140

C₂×C₃×D₉

—

141

C₂×C₃×D₉

—

142

C₃⁴

C₂×C₃×D₃

yes

143

C₃²×C₉

—

144

C₃²×C₉

—

145

C₃²×C₉

—

146

C₃²×C₉

—

147

C₃²×C₉

—

148

C₃²×C₉

—

149

C₃²×C₉

—

150

C₃²×C₉

—

151

C₃²×C₉

—

152

C₃²×C₉

—

153

C₃²×C₉

—

154

C₃²×C₉

—

155

C₃²×C₉

—

156

C₃²×C₉

C₂×C₃×D₃

yes

157

C₃²×C₉

C₂×C₃×D₃

yes

158

C₃²×C₉

C₂×C₃×D₃

yes

159

C₃²×C₉

C₂×C₃⋊D₃

yes

160

C₉⋊C₉

—

161

C₉⋊C₉

—

162

C₉⋊C₉

—

163

C₉⋊C₉

—

164

C₉⋊C₉

—

165

C₉⋊C₉

—

166

C₉⋊C₉

—

167

C₉⋊C₉

—

168

C₉⋊C₉

—

169

C₃²⋊C₉

—

170

C₃²⋊C₉

—

171

C₃²⋊C₉

—

172

C₃²⋊C₉

—

173

C₃²⋊C₉

—

174

C₃²⋊C₉

—

175

C₃²⋊C₉

—

176

C₃²⋊C₉

C₂²×C₉

yes

177

C₂×C₃³

—

178

C₂×C₃³

—

179

C₂×C₃³

—

180

C₂×C₃³

—

181

C₂×C₃³

—

182

C₂×C₃³

—

183

C₂×C₃³

—

184

C₂×C₃³

—

185

C₂×C₃³

—

186

C₂×C₃³

—

187

C₂×C₃³

D₃×C₉

yes

188

C₂×C₃³

AGL(1,ℤ/9)

yes

189

C₂×C₃³

AGL(1,ℤ/9)

yes

190

C₂×C₃³

AGL(1,ℤ/9)

yes

191

C₂×C₃³

C₃×C₃⋊D₃

yes

192

C₃×C₃⋊D₃

—

193

C₃×C₃⋊D₃

—

194

C₃×C₃⋊D₃

—

195

C₃×C₃⋊D₃

—

196

C₃²×D₃

—

197

C₃²×D₃

—

198

C₃²×D₃

—

199

C₃²×D₃

—

200

C₂×C₃×C₉

—

201

C₂×C₃×C₉

—

202

C₂×C₃×C₉

—

203

C₂×C₃×C₉

—

204

C₂×C₃×C₉

—

205

C₂×C₃×C₉

—

206

C₂×C₃×C₉

—

207

C₂×C₃×C₉

—

208

C₂×C₃×C₉

—

209

C₂×C₃×C₉

—

210

C₂×C₃×C₉

—

211

C₂×C₃×C₉

—

212

C₂×C₃×C₉

—

213

C₂×C₃×C₉

—

214

C₂×C₃×C₉

—

215

C₂×C₃×C₉

—

216

C₂×C₃×C₉

—

217

C₂×C₃×C₉

—

218

C₂×C₃×C₉

—

219

C₂×C₃×C₉

—

220

C₂×C₃×C₉

—

221

C₂×C₃×C₉

—

222

C₂×C₃×C₉

—

223

C₂×C₃×C₉

—

224

C₂×C₃×C₉

—

225

C₂×C₃×C₉

—

226

C₂×C₃×C₉

—

227

C₂×C₃×C₉

—

228

C₂×C₃×C₉

—

229

C₂×C₃×C₉

—

230

C₂×C₃×C₉

—

231

C₂×C₃×C₉

—

232

C₂×C₃×C₉

—

233

C₂×C₃×C₉

—

234

C₂×C₃×C₉

—

235

C₂×C₃×C₉

—

236

C₂×C₃×C₉

—

237

C₂×C₃×C₉

—

238

C₂×C₃×C₉

—

239

C₂×C₃×C₉

—

240

C₂×C₃×C₉

—

241

C₂×C₃×C₉

—

242

C₂×C₃×C₉

—

243

C₂×C₃×C₉

—

244

C₂×C₃×C₉

—

245

C₂×C₃×C₉

—

246

C₂×C₃×C₉

—

247

C₂×C₃×C₉

—

248

C₂×C₃×C₉

—

249

C₂×C₃×C₉

—

250

C₂×C₃×C₉

—

251

C₂×C₃×C₉

D₃×C₉

yes

252

C₂×C₃×C₉

D₃×C₉

yes

253

C₂×C₃×C₉

D₃×C₉

yes

254

C₂×C₃×C₉

#272

yes

255

C₂×C₃×C₉

#272

yes

256

C₂×C₃×C₉

#272

yes

257

D₃×C₉

—

258

D₃×C₉

—

259

D₃×C₉

—

260

D₃×C₉

—

261

D₃×C₉

—

262

D₃×C₉

—

263

D₃×C₉

—

264

D₃×C₉

—

265

D₃×C₉

—

266

D₃×C₉

—

267

D₃×C₉

—

268

D₃×C₉

—

269

C₃×D₉

—

270

C₃×D₉

—

271

C₃×D₉

—

272

C₃×D₉

—

273

C₃×D₉

—

274

C₃×D₉

—

275

C₃×D₉

—

276

C₃×D₉

—

277

C₃×D₉

—

278

C₃×D₉

—

279

C₃×D₉

—

280

C₃×D₉

—

281

C₂²×C₃²

—

282

C₂×C₃⋊D₃

—

283

C₂×C₃×D₃

—

284

C₂×C₃×D₃

—

285

C₂×C₃×D₃

—

286

C₂×C₃×D₃

—

287

C₂×C₃×D₃

—

288

C₂×C₃×D₃

—

289

C₂×C₃×D₃

—

290

C₂×C₃×D₃

—

291

C₂×C₃×D₃

—

292

C₂×C₃×D₃

—

293

C₂×C₃×D₃

—

294

C₂×C₃×D₃

—

295

C₂×C₃×D₃

—

296

C₂×C₃×D₃

—

297

C₂×C₃×D₃

—

298

C₂×C₃×D₃

—

299

C₂²×C₉

—

300

C₂²×C₉

—

301

C₂²×C₉

—

302

C₂×D₉

—

303

C₂×D₉

—

304

C₂×D₉

—

305

C₃³

—

306

C₃³

—

307

C₃³

—

308

C₃³

—

309

C₃³

—

310

C₃³

—

311

C₃³

—

312

C₃³

—

313

C₃³

—

314

C₃³

—

315

C₃³

C₂×D₃×C₉

yes

316

C₃³

C₂×AGL(1,ℤ/9)

yes

317

C₃³

C₂×AGL(1,ℤ/9)

yes

318

C₃³

C₂×AGL(1,ℤ/9)

yes

319

C₃³

C₂×C₃×C₃⋊D₃

yes

320

C₃×C₉

—

321

C₃×C₉

—

322

C₃×C₉

—

323

C₃×C₉

—

324

C₃×C₉

—

325

C₃×C₉

—

326

C₃×C₉

—

327

C₃×C₉

—

328

C₃×C₉

—

329

C₃×C₉

—

330

C₃×C₉

—

331

C₃×C₉

—

332

C₃×C₉

—

333

C₃×C₉

—

334

C₃×C₉

—

335

C₃×C₉

—

336

C₃×C₉

—

337

C₃×C₉

—

338

C₃×C₉

—

339

C₃×C₉

—

340

C₃×C₉

—

341

C₃×C₉

—

342

C₃×C₉

—

343

C₃×C₉

—

344

C₃×C₉

—

345

C₃×C₉

—

346

C₃×C₉

—

347

C₃×C₉

—

348

C₃×C₉

—

349

C₃×C₉

—

350

C₃×C₉

—

351

C₃×C₉

—

352

C₃×C₉

—

353

C₃×C₉

—

354

C₃×C₉

—

355

C₃×C₉

—

356

C₃×C₉

—

357

C₃×C₉

—

358

C₃×C₉

—

359

C₃×C₉

—

360

C₃×C₉

—

361

C₃×C₉

—

362

C₃×C₉

—

363

C₃×C₉

—

364

C₃×C₉

—

365

C₃×C₉

—

366

C₃×C₉

—

367

C₃×C₉

—

368

C₃×C₉

—

369

C₃×C₉

—

370

C₃×C₉

C₂×D₃×C₉

yes

371

C₃×C₉

C₂×D₃×C₉

yes

372

C₃×C₉

C₂×D₃×C₉

yes

373

C₃×C₉

C₂×#272

yes

374

C₃×C₉

C₂×#272

yes

375

C₃×C₉

C₂×#272

yes

376

C₂×C₃²

—

377

C₂×C₃²

—

378

C₂×C₃²

—

379

C₂×C₃²

—

380

C₂×C₃²

—

381

C₂×C₃²

—

382

C₂×C₃²

—

383

C₂×C₃²

—

384

C₂×C₃²

—

385

C₂×C₃²

—

386

C₂×C₃²

—

387

C₂×C₃²

—

388

C₂×C₃²

—

389

C₂×C₃²

—

390

C₂×C₃²

—

391

C₂×C₃²

—

392

C₂×C₃²

—

393

C₂×C₃²

—

394

C₂×C₃²

—

395

C₂×C₃²

—

396

C₂×C₃²

—

397

C₂×C₃²

—

398

C₂×C₃²

—

399

C₂×C₃²

—

400

C₂×C₃²

—

401

C₂×C₃²

—

402

C₂×C₃²

—

403

C₂×C₃²

—

404

C₂×C₃²

—

405

C₂×C₃²

—

406

C₂×C₃²

D₉⋊C₉

yes

407

C₂×C₃²

D₉⋊C₉

yes

408

C₂×C₃²

D₉⋊C₉

yes

409

C₂×C₃²

C₉×C₃⋊D₃

yes

410

C₂×C₃²

C₃×#272

yes

411

C₂×C₃²

C₃⋊AGL(1,ℤ/9)

yes

412

C₂×C₃²

#4208

yes

413

C₂×C₃²

#4208

yes

414

C₃⋊D₃

—

415

C₃×D₃

—

416

C₃×D₃

—

417

C₃×D₃

—

418

C₃×D₃

—

419

C₃×D₃

—

420

C₃×D₃

—

421

C₃×D₃

—

422

C₃×D₃

—

423

C₃×D₃

—

424

C₃×D₃

—

425

C₃×D₃

—

426

C₃×D₃

—

427

C₃×D₃

—

428

C₃×D₃

—

429

C₃×D₃

—

430

C₃×D₃

—

431

C₂×C₉

—

432

C₂×C₉

—

433

C₂×C₉

—

434

C₂×C₉

—

435

C₂×C₉

—

436

C₂×C₉

—

437

C₂×C₉

—

438

C₂×C₉

—

439

C₂×C₉

—

440

C₂×C₉

—

441

C₂×C₉

—

442

C₂×C₉

—

443

C₂×C₉

—

444

C₂×C₉

—

445

C₂×C₉

—

446

C₂×C₉

—

447

C₂×C₉

—

448

C₂×C₉

—

449

D₉

—

450

D₉

—

451

D₉

—

452

C₂²×C₃

—

453

C₂²×C₃

—

454

C₂²×C₃

—

455

C₂²×C₃

—

456

C₂×D₃

—

457

C₂×D₃

—

458

C₂×D₃

—

459

C₂×D₃

—

460

C₃²

—

461

C₃²

—

462

C₃²

—

463

C₃²

—

464

C₃²

—

465

C₃²

—

466

C₃²

—

467

C₃²

—

468

C₃²

—

469

C₃²

—

470

C₃²

—

471

C₃²

—

472

C₃²

—

473

C₃²

—

474

C₃²

—

475

C₃²

—

476

C₃²

—

477

C₃²

—

478

C₃²

—

479

C₃²

—

480

C₃²

—

481

C₃²

—

482

C₃²

—

483

C₃²

—

484

C₃²

—

485

C₃²

—

486

C₃²

—

487

C₃²

—

488

C₃²

—

489

C₃²

C₂×D₉⋊C₉

yes

490

C₃²

C₂×D₉⋊C₉

yes

491

C₃²

C₂×D₉⋊C₉

yes

492

C₃²

C₂×C₉×C₃⋊D₃

yes

493

C₃²

C₂×C₃×#272

yes

494

C₃²

C₂×C₃⋊AGL(1,ℤ/9)

yes

495

C₃²

C₂×#4208

yes

496

C₃²

C₂×#4208

yes

497

C₉

—

498

C₉

—

499

C₉

—

500

C₉

—

501

C₉

—

502

C₉

—

503

C₉

—

504

C₉

—

505

C₉

—

506

C₉

—

507

C₉

—

508

C₉

—

509

C₉

—

510

C₉

—

511

C₉

—

512

C₂×C₃

—

513

C₂×C₃

—

514

C₂×C₃

—

515

C₂×C₃

—

516

C₂×C₃

—

517

C₂×C₃

—

518

C₂×C₃

—

519

C₂×C₃

—

520

C₂×C₃

—

521

C₂×C₃

—

522

C₂×C₃

—

523

C₂×C₃

—

524

C₂×C₃

—

525

C₂×C₃

—

526

C₂×C₃

C₃⋊(D₉⋊C₉)

yes

527

C₂×C₃

C₉×#272

yes

528

C₂×C₃

#92302

yes

529

C₂×C₃

#6895⋊C₂

yes

530

C₂×C₃

#6895⋊C₂

yes

531

D₃

—

532

D₃

—

533

D₃

—

534

D₃

—

535

C₂²

—

Sylow

536

C₃

—

537

C₃

—

538

C₃

—

539

C₃

—

540

C₃

—

541

C₃

—

542

C₃

—

543

C₃

—

544

C₃

—

545

C₃

—

546

C₃

C₂×C₃⋊(D₉⋊C₉)

yes

547

C₃

C₂×C₉×#272

yes

548

C₃

C₂×#92302

yes

549

C₃

C₂×#6895⋊C₂

yes

550

C₃

C₂×#6895⋊C₂

yes

551

C₂

—

552

C₂

characteristic, direct product factor

yes

	subgroup	G/H
center, hypercenter	C₂×C₃²	C₃⋊AGL(1,ℤ/9)
commutator, hypocenter	C₃²⋊C₉	C₂²×C₉
Frattini	C₃³	C₂×C₃×C₃⋊D₃
Fitting	C₂×#10624556	C₂
socle	C₂×C₃³	C₃×C₃⋊D₃
prime radical	C₂×C₃×#4181	C₃
cosocle	C₃×C₃²⋊C₉	C₂²×C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂×C₃²

subgroup

G/H

center, hypercenter

C₂×C₃²

C₃⋊AGL(1,ℤ/9)

commutator, hypocenter

C₃²⋊C₉

C₂²×C₉

Frattini

C₃³

C₂×C₃×C₃⋊D₃

Fitting

C₂×#10624556

C₂

socle

C₂×C₃³

C₃×C₃⋊D₃

prime radical

C₂×C₃×#4181

C₃

cosocle

C₃×C₃²⋊C₉

C₂²×C₃

LCS

G ▷ C₃²⋊C₉

UCS

C₁ ◁ C₂×C₃²

N	H ≅ G/N	type
1. #13090646	C₂	direct (N × H)
2. C₂×#10624556	C₂	semidirect
8. #10624556	C₂²	semidirect
11. C₂×C₃×C₉⋊C₉	D₃	semidirect
12. C₂×C₃×C₉⋊C₉	D₃	semidirect
13. C₂×C₃×C₉⋊C₉	D₃	semidirect
34. C₂×#4181	C₉	semidirect
45. C₃×C₉⋊C₉	C₂×D₃	semidirect
46. C₃×C₉⋊C₉	C₂×D₃	semidirect
47. C₃×C₉⋊C₉	C₂×D₃	semidirect
98. C₂×C₃²⋊C₉	C₂×C₉	semidirect
99. #4181	C₂×C₉	semidirect
176. C₃²⋊C₉	C₂²×C₉	semidirect
251. C₂×C₃×C₉	D₃×C₉	semidirect
252. C₂×C₃×C₉	D₃×C₉	semidirect
253. C₂×C₃×C₉	D₃×C₉	semidirect
370. C₃×C₉	C₂×D₃×C₉	semidirect
371. C₃×C₉	C₂×D₃×C₉	semidirect
372. C₃×C₉	C₂×D₃×C₉	semidirect
406. C₂×C₃²	D₉⋊C₉	semidirect
407. C₂×C₃²	D₉⋊C₉	semidirect
408. C₂×C₃²	D₉⋊C₉	semidirect
489. C₃²	C₂×D₉⋊C₉	semidirect
490. C₃²	C₂×D₉⋊C₉	semidirect
491. C₃²	C₂×D₉⋊C₉	semidirect
552. C₂	#13090646	direct (N × H)

H ≅ G/N

type

1. #13090646

C₂

direct (N × H)

2. C₂×#10624556

C₂

semidirect

8. #10624556

C₂²

semidirect

11. C₂×C₃×C₉⋊C₉

D₃

semidirect

12. C₂×C₃×C₉⋊C₉

D₃

semidirect

13. C₂×C₃×C₉⋊C₉

D₃

semidirect

34. C₂×#4181

C₉

semidirect

45. C₃×C₉⋊C₉

C₂×D₃

semidirect

46. C₃×C₉⋊C₉

C₂×D₃

semidirect

47. C₃×C₉⋊C₉

C₂×D₃

semidirect

98. C₂×C₃²⋊C₉

C₂×C₉

semidirect

99. #4181

C₂×C₉

semidirect

176. C₃²⋊C₉

C₂²×C₉

semidirect

251. C₂×C₃×C₉

D₃×C₉

semidirect

252. C₂×C₃×C₉

D₃×C₉

semidirect

253. C₂×C₃×C₉

D₃×C₉

semidirect

370. C₃×C₉

C₂×D₃×C₉

semidirect

371. C₃×C₉

C₂×D₃×C₉

semidirect

372. C₃×C₉

C₂×D₃×C₉

semidirect

406. C₂×C₃²

D₉⋊C₉

semidirect

407. C₂×C₃²

D₉⋊C₉

semidirect

408. C₂×C₃²

D₉⋊C₉

semidirect

489. C₃²

C₂×D₉⋊C₉

semidirect

490. C₃²

C₂×D₉⋊C₉

semidirect

491. C₃²

C₂×D₉⋊C₉

semidirect

552. C₂

direct (N × H)

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

subgroup	index
#13090646	2
C₂×#10624556	2
C₂×C₃×C₉×C₃⋊D₃	3
C₂×C₃×#4181	3
C₂×C₃×D₉⋊C₉	3

subgroup

index